1.11: Life Occurs in Sharp Spikes
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This article theorizes that attention is not linear. That is almost obvious, however, because when you look at a room full of objects your attention must fluctuate many times just then as you go from object to object. The question is, what is your conscious awareness of what you are paying attention to? If you look at it from that perspective, your attention doesn't change that much because you are not aware of that many major changes. If you look at it from an unconscious perspective, your attention fluctuates greatly all the time, with minor variations in how you are processesing everything. Are someones unconcsious fluctuations in attention important, however? When someone first starts paying attention to something do they have to pay more attention at the start to bring the object into cognition? Is it necessary to pay sharp attention to things every so often because you need to be kept awake? This chapter tries to show that your unconcsious attention must pay sharp attention to things in spikes in order to a) keep noticing things and b) stay sharp. However, if people might are not aware that they need to refocus on objects, then how important and significant is this refocusing of your attention in a spike pattern?
People need to pay attention to things in order to keep their minds alive and active. They need to pay attention to little things all the time. That is why spikes occur, when people refocus their attention on little things over and over it occurs as a spike, because the new object needs to be processed as a whole and this processing takes energy in the form of a “spike”. [The key thing there is that the object needs to be processed as a whole.
Humans cannot pay attention to everything, and the things they do pay attention to they need to “spike” their attention initially to get that object into their attention and focus. It is possible to not use spikes of attention, but if you did that then life would be boring. In order for life to be interesting people naturally spike their attention on certain things every so often (once a minute or so) to make life more exciting. Life would be boring if you never paid sharp attention to anything. Spikes of attention keep life “crisp”. [You could rephrase that as, if you never pay attention to anything, you are never going to be interested in anything. And if you actually pay attention to something, you would need to direct your attention to it at some point, putting in maximum attention so you grab it into focus, that is the spike.]
A good example of a spike in attention is if you direct your attention to something that is going to be shown to you for only a short period of time. For instance in a study by Sperling (1960) found that when subjects were presented with visual arrays lasting 50ms, containing twelve letters, they were able to report only about four or five items. However, subjects said they could "see" the whole display for a short time after the display was terminated. That shows how it is possible for people to direct high attention to be able to pay attention to something for that short a period of time, but also that this attention will die down very quickly after it was given – shown by the fact that they forgot what they saw soon after.
If life occurs in sharp spikes, why then doesn’t it feel like life occurs in sharp spikes? It seems pretty smooth to me. If it seems this way, then you aren’t realizing or paying attention to the complicated emotional and cognitive processes that are going on in your mind, life is not “all smooth” but there are changes in attention going on all the time. Each little thing you pay attention to (actually pay attention to that is, not just “absorb”) actually occurs as a spike in attention. This is because most of the time your attention isn’t extremely directed, but you need to make it extremely directed sometimes (once a minute or so) in order to properly stay awake. It is also because you don’t absorb every little thing, you only absorb a few things once in a while, and these things that you do absorb are the spikes. They are spikes because they are relative to most of your activity which isn’t absorbing things intently or deeply. Every minute or so you need to absorb something. That thing is the spike. [People think all the time, and since thinking is an intense activity (we defined it as a period of high attention), it needs to be supported by intense activities, and a spike is one of these activities. So you could spike your attention on a thought, or use a thought to pay attention to a vision, etc.]
When you pay attention to your attention (or what you are paying attention to) how does life feel to you? Does it feel smooth or rough? Life seems rough if you pay attention to it like that, with occasional spikes of interest in things. It is rough because there are many little fluctuations of interest in various things, but intensity is needed somewhere. This intensity comes from the spikes, otherwise life would just be rough and there wouldn’t be anything smooth. The top of the spike is smooth, however because it is clear and it lasts a little while (a few seconds or a few dozen seconds). Paying sharp attention to things allows you to have a clear mind for the time you are giving that sharper attention. It separates out all the other things and you focus more on what it is you processed. This clears your mind because you just received a lot of stimulation. In this way spikes can make life be smooth. Without spikes life would always be rough because of all the little things. But if you use a spike then life is smooth afterwards because you are satisfied. [So emotional stimulation could come from the spikes, since they are significant since you are paying a lot of attention they might generate more emotion. This emotion helps you to focus on the thing you are trying to pay attention to because you're more interested in it. Since you're paying attention to something now, you don't need to pay attention to other things, so life is smooth because you are being occupied. (not rough by lots of little things you're not really paying attention to) - that applies to various strengths of spikes, whether it is just focusing on something small or a significant amount of emotion or focus generated from something large]
Life is many small variations in attention over time. There are periods of focused attention and periods of non-focused attention. The periods of focused attention are the spikes. This is very complicated if you try to follow your own spikes because there are so many things you are “spiking” and paying sharp attention to all the time. There are three groups of things, things you pay sharp attention to, things you pay attention to, and things you don’t pay attention to. You pay sharp attention to things much less often than the other two categories, and that is why the sharp attention is a spike, because it is uncommon and doesn’t last as long as the other things, so it looks more like a spike when compared with the other two categories than a leveled plain. [You might have little spikes then, things you pay a little attention to. Most of the time you're not paying attention to things, or paying attention in a steady form. But when that attention starts it is grabbed because it is something new, and if it is something new that you're not going to be paying attention to much after processing it, then it might just be a small spike because you stop paying attention to it before your interest can grow.]
Also, people’s emotions change all the time. The change probably occurs both gradually and like a series of steps. There are so many emotions in a person’s head that some of them are going to interact with each other suddenly, causing a sudden sharp change in emotion, and others are going to interact more slowly, causing gradual changes in emotion. [So some changes might even be spikes.]
It might be that the changes are just sharp, however. You could look at the mind as a system that only changes when it gets a trigger, and that would probably mean that it only has sharp changes of emotion. However those changes wouldn’t just be sharp changes. Large, sharp changes of emotion don’t just happen by themselves, but deep emotional experiences are often followed by similar emotions that are less intense. That is, if you experience emotion A, emotion A is going to linger in your system. [That is, you would need a spike to produce a major change, but a minor change might be induced by a smaller spike (but still a spike relative to the emotion after the change) so emotional spikes would work like attentional spikes, starting with a spike because there is an initial period of interest.]
That excludes the staircase model, but there still could be something like a staircase, only instead of steps at a 90 degree angle they would be something like an 100 degree angle. With 10/360 percent being the emotions that hang around after an initiating event. That would be just emotion changes resulting from large events, however. Either a large event within your own system (something like a thought or a feeling, or a mix of thoughts and feelings), or a large external event (like something happening outside your body). [So an attentional spike might result in an emotional spike, or vice versa.] That’s because your mind needs to understand, “ok now I am sad”. As intellectual, thinking beings all major emotional events that occur in the mind need to processed intellectually (unless you’re sleeping). So in other words if you just get sadder and sadder and are not aware of it you are not going to get nearly as sad as when you realize that you are getting sadder. The points when you realize (at some level) that you are getting sadder are going to be when you start feeling a lot sadder (the steps on the downward staircase of sadness and depression).
There must be other stuff going on in the mind, however. While a clash or mix of two feelings or emotions or thoughts could be figured out, and that would probably result in a noticeable emotional change (the staircase or spike model). There are probably other things going on in your conscious or unconscious mind. That is, some things that happen to people take a long time to recover from. But the main point is, everything, whether or not is a slow, gradual change or a sudden, quick change, resulted from some mix of emotions and feelings and thoughts and external events happening.
Furthermore, any mix of those things, when they interact, is going to be a large change. That is because it is a large change relative to your normal state, which is most of the time feeling nothing, because nothing is going on most of the time. People experience events in life and things in life and they occur in individual units.
Thoughts, emotions, and feelings are the three main components of the brain.  There is vision, that is, you see things all the time, but your emotion doesn’t go up or down a lot when you close or open your eyes. Unless you are looking at something that is causing a feeling, of course. But even then that feeling is only going to last a few seconds before it dies off. Therefore vision clearly functions with the sharp spikes pattern.
The same with hearing, if you hear something interesting, there is a sharp spike of initial interest, and then it dies down to almost normal. That must mean that feelings and emotions are probably a combination of thoughts, feelings, and emotions. That you almost think about the event that is occurring, and that when you think about it there is a large spike upwards. That the combination of feeling and emotion with thought results in large spikes, which form our best and common regular life experiences. [So in other words, the spikes are like thoughts because they are a period of high attention (which we defined thought as) even though they might be mostly emotional, they can still be like thoughts as well.]
That is, you can’t really tell you are thinking about it because it isn’t verbal. But it feels like you are thinking about it during that brief time. That means that your attention is going to be focused on it, basically. Sometimes when someone is in a depression these spikes can be very large because that person is very upset. A large spike would result in emotional damage, furthering the depression, thereby causing the depression to go down like a staircase. It is easy to do emotional damage, but it can’t be repaired in a series of spikes, as it would go up gradually (still small compared to the spikes however). [So if you are going through a hard time, what makes that time hard might not just be a higher level of sadness, but there might be more complicated traumatic feelings which are intense mixed in (like spikes).]
Just think of it as fabric; damage needs to be mended, and mending takes time. It is easy to do damage to the fabric, you can only mend it slowly. No one just “snaps out” of a depression. Furthermore it is easy to stimulate the fabric, just poke it. That poke would be similar to a life experience, the poke has ripples, but the main event was the poking. [So spikes are significant beyond just the spike, they can help you to pay attention to what you spiked, or cause damage if it was a negative spike.]
The sharp spike occurrences show just how short of attention span humans have. That for brief periods we are capable of almost perfect attention, and during those periods is the height of the spikes. These spikes actually look more like lumps since they go up gradually and cause a stay in attention for a few seconds, but they are so fast that they are best called spikes. Say looking at an attractive girl/guy causes a feeling. The first few seconds you look at her/him, you are going to have perfect attention, but then it is going to die off. Everything else in life is somewhat like that, whether you are looking at your pencil, or your computer, or whatever. The item you are looking at needs to be initially processed, and your attention needs to be directed to it first off.
Everything in life needs to be processed before it enters your system, and that process is going to be a sharp spike of emotion, feeling, and thought. After you process looking at the computer you can move along to just wandering your eyes throughout the room. If you pause at any one of the things you are wandering your eyes around, you will experience a sharp spike of emotion/thought/feeling. That is, looking at things also causes emotion as well as the thought needed to direct your attention to it, if you are paying more attention to something which causes emotion, then logically you are going to feel more emotion from it.
This doesn’t mean that you aren’t thinking/feeling when you don’t pause or stop. You could say that people are thinking, feeling, and are having emotion all of the time just in amounts so small it is hard for them to detect. That these amounts only go up in sharp spikes when they actually pay attention to something either in their mind or outside it. This “paying attention” doesn’t have to be conscious or deliberate. If two feelings interact within your mind it could cause you to pay conscious or unconscious attention to them.
Something like, your girlfriend meeting your ex girlfriend would cause a clash of feelings for your new girlfriend, with feelings for your old girlfriend (possibly). But that clash of feelings wouldn’t occur in a thought spike, it would occur in an emotional spike. It would also be a slight rise of tension in the feeling between which one you like more. Also, the rise in that feeling wouldn’t be significant compared to if you thought about that feeling at the same time. When you think about the feeling it would result in a sharp spike, and that spike would last a few seconds, then die away. That is because that feeling was a potential explosive one, one that exploded when you thought about it, resulting in a spike. Also, thought about anything else, a feeling, a vision, whatever, results in lesser spikes of thoughts/feelings/emotions. That anything and everything, when thought about, is interesting for the first few seconds, but then that interest dies off. It is the same principal when you pinch yourself. When you pinch yourself the first time, it hurts the most. That is because the first time you are thinking about it a lot more, after that your interest in it dies off. Amazing how much our attention can fluctuate to cause life to occur in short, sharp spikes. [So some experiences and emotions can produce spikes easier than others. Though an emotional spike like in that example isn't a "fast" one that just grabs attention, but is one that stays around as high attention for a while. There are minor spikes when you grab your attention to something or have an emotional change, and there are longer ones where you stayed "grabbed" for a while.] The girlfriend example is different than spikes that occur more frequently all the time, when you pay attention to little things. The girlfriend example was an example of when a spike can happen, but that is a spike that you are going to notice a lot more then something like, you just refocusing on what you are typing. It is spikes like that which happen all the time so you stay focused.
Although there are spikes of emotion and feeling, spikes of thought are needed to direct attention. Not thought in the verbal sense, but thought in the sense that it is under your control and feels more similar to thoughts. Thought occurs as basically a bunch of spikes, and since people think all the time and about everything, life occurs in those spikes. They don’t feel intense because it is just thought. But basically whenever something new comes into your vision or your attention there is an initial sharp spike of interest. And if you are going to be doing the same thing for a long period of time, then it is going to take additional sharp spikes every couple of seconds or every minute to keep your attention. It is easy to test that, try and read something with the same bland expression as when you start reading it (but after your initial interest at the beginning when you notice the piece) and you just can’t do it. To maintain attention your mind needs to snap back to what it is paying attention to. Feelings and emotions are going to follow the thought, however (that is emotions and feelings are imbedded in thoughts). That is why people need to think all the time, to maintain a healthy level of mental activity, it is a part of life. Emotions and feelings can also be described as thoughts, however, so those spikes continue even after you stop thinking, just in the form of emotion-feeling-thoughts (they are still more similar to thoughts however since they are short and spiky). [So a "thought" is required to direct attention. That is because to direct attention you need to pay sharp attention, and any thought is something which you are paying attention to. Something could grab your attention unconsciously, and it could be more like an unconscious thought that pulls you in. That shows that there is going to be degrees of consciousness to which your attention is grabbed, sometimes you do it deliberately, and sometimes you spike your attention without thinking about it at all.]
Basically your attention needs to be initially “grabbed” for anything that you are going to pay attention to. That grabbing is the initial period of paying attention to it. During that first period of paying attention to something is where the spike is because you are processing the item/object. You need a spike to grab your mind and attention, otherwise you wouldn’t be paying attention to anything. You can still process most of life without the spikes, but that is only because spikes had brought you back to reality in the first place in order for that attention to be grabbed. Furthermore it is going to be easier to process new things based on what the spike was about, that is, it is going to be easier to process similar things more related to the spike then to other things in the area. If you focus on a school bus, then you are going to be more attentive to the other school buses you see for the next few seconds or minutes because you were just paying attention to one school bus, and your mind is wired to notice school buses. [That is because you are probably going to have a higher emotional interest in the school bus, making you more aware of it. Even if the thing you saw generated a negative emotion, you still would pay more attention to it (unconsciously) because you are alerted to it. It is in your mind, so when you see it you can process it better.] A study shows that prior experience of a semantically associated word such as "doctor" speeds up naming to a subsequent related probe word such as "nurse" (Meyer & Schavaneveldt. 1972).
Furthermore there is a similar way in which your mind processes each spike. For spikes that are under your control, first the spike would be a period of thought about something, say a school bus or a coffee machine. Then what you just saw or thought about becomes an emotion, or an unconscious series of thoughts. That is you are less focused consciously on what it is you are seeing or whatever but your mind is still processing it. Next, after your mind processes the unconscious thoughts it becomes a feeling, you then feel something about what it is you were focusing on. So it isn’t when you look at something you immediately get a feeling, that doesn’t make any sense. First you think about it, then you feel it in a general way (an emotion) then after you understand what that feeling is, you feel it (but that basically happens instantaneously so in a way you do feel it right away - also, that same process can happen over a longer period of time). That is because you know what it is, you know where it is, and you know what to focus your attention on. An example of unconsciously processing something you see is when you look at match you then think about fire. Then after you think about the fire you can almost “feel” the fire, following the pattern of thought to emotion to feeling (you think about the match, then something happens unconsciously (this unconscious thought process is emotion (remember emotion is unconscious thought) which then causes you to feel the fire – a feeling). [Not everyone is going to feel fire when they look at a match, and for the people that do, that feeling is probably going to be unconscious. That was just an example of how things can be thought about more than just what they are, and since they are going to be thought about, they are going to go from thought to emotion to feeling (emotion more similar to thought than feeling). Since it is a spike of thought that directs attention, the spike dies off, so it goes from thought to emotion, since the emotion is less intense than the thought, after the thought period (or the spike period) you don't need to think about it anymore since you already processed it consciously, you simply then think about it further unconsciously - that thinking unconsciously is the final part where it is a just a small feeling (so it goes from thought to emotion to feeling (with some overlap). Emotion is more like almost consciously thinking about something compared to feeling.
It could be that a few minutes passes before a conscious spike occurs (that is a spike that is under your control). A spike is basically just anything that you are going to start paying attention to. During those first few seconds of when you are going to pay attention to something there is a sharp spike upwards. Without these periods of attention humans/animals would never pay attention to anything. Basically once every few minutes or so you need to pay attention to something or your brain is going to be too inactive. After you pay attention to one thing, however, your general attention is grabbed and you don’t need to have another spike for at least a few minutes.
Everything that is processed, not just spikes, follows the sequence of thought to emotion to feeling. That is because thoughts are clearer than emotions and feelings, and emotions are more similar to thoughts than feelings are (discussed previously) so when you see something or hear something or whatnot for the first time, it is clearer in your mind. Then it becomes less clear and you think about it unconsciously. You think about it unconsciously because it takes further processing in order to isolate the feeling that that things gives you. Some things are just too complicated to feel them right away. Other things, however, can be felt right away, say if you are touching something the feeling arises right away. That is because the physical stimulus is more immediate than emotional stimulus. [Emotion is very complicated, so the emotions something gives you you aren't going to understand well (for instance a feeling of depression is very complicated but the feeling of sadness that comes from it isn't that emotion lead to a more simple feeling). That also shows how this thought-emotion-feeling pattern occurs quickly, and is just based off of the thought period "dying off" and becoming less and less like a thought, and more and more like a feeling. You could think about it later and spike it again, and then the series would repeat. This doesn't mean that everything occurs as thought to emotion to feeling, only when you have a thought the thought is going to be brief, and when it goes away a feeling is left. Feelings and emotions last longer than thoughts (in fact, you're feeling all the time, but only thinking specific things some of the time).]
Emotional things, however, are simply to complicated to “feel” them right away, they need to be processed first. That is logical, just take looking at anything, say a book. In order to feel the feelings that the book causes in you, you are going to have to at least unconsciously think about it first (that is, after you start paying attention to it, which you do by starting to think about it or just see it and notice it more than you usually notice things in the area). Since you don’t need to think about physical stimulus since it is just a physical stimulus, (not something like vision) you don’t really unconsciously process it.
Spikes are dramatic rises in attention. They can be assisted by load noises or something dramatic visually, but they don’t need to be. In other words they can be internal or external. You can pay sharp attention to something in the real world or something in your own head. If there is a load sound in the environment, it is most likely that your spike in attention is going to occur during that period. It doesn’t have to, you could pay attention to something else in spike form, but the main point is that you have to have about one sharp spike in attention a minute at least. That is, you have to pay attention to something in your environment or something in your head, sharp attention in the form of a spike (lasting a second or a few seconds) every minute or so.
Otherwise the world would just go by you and you’d be completely out of it. You don’t just need to pay attention to things, you occasionally need to pay sharp attention to things. Furthermore this attention in the form of a spike can’t be dissipated and spread out, it is always going to occur in a spike. If, in between the spikes, you are trying to get the highest attention you can in an attempt to spread the spike out, (that is, if you are trying to spread out your attention instead of having spikes) the normal spike would still be a spike relative to even the extra attention you gave to the non spike period, because that attention would still be too low, so you couldn’t give it that high of an attention level, as it would be very low compared to the spike still. Spikes of emotion and feeling also need to occur every few minutes or so. The human system needs to be “shocked” into reality because you need to pay attention to life.
Say it is time for another sharp increase in attention (that is you waited too long without focusing on anything) and something occurs like a dog barking. Then you are going to focus on that dog barking intently in the form of a spike. So if the dog continues to bark for the next few seconds or minutes, your attention will be on that more because you paid attention to it initially more so than other things in your environment. This is very important because if someone doesn’t use their spikes say to someone they are talking to, they could be talking to that person and not be paying attention at all. You could hear what they are saying but not really be interested in it nearly as much as you would in a normal conversation (if you choose not to think about the person talking to you – remember if you do think about the person talking to you then naturally you are going have a thought spike because that is how thought initiates when thinking about new objects, the new object needs to be grabbed and processed first).
If you direct your attention spikes away from the things you don’t want to hear (say if there is a loud noise in the background, just don’t pay sharp attention to it) then most of your attention will follow along suit. If attention was uniform then people wouldn’t be able to direct their attention easily. In order to ignore the other things in your environment and just focus on one thing, the only way to get just that one thing into your focus would be to use a spike in attention. After that spike the thing you “spiked” would be in your attention at a low level, but the other things around you would be at an even lower level. The spike is necessary to differentiate what you are paying attention to, to differentiate the new thing which you are paying attention to from everything else. You can’t just go to a slightly higher rise in attention for one thing (you can pay attention to something new, but you wouldn’t be paying more attention to it than other things in the environment already, you’d just be isolating that thing, it wouldn’t be a rise in attention, or an insignificant one), because people can only focus on one thing at a time for this reason. Because of the spikes in attention, people can isolate (focus intently on) one or a few things.
That limitation (of only being able to focus intently on a few things) happens because each spike eliminates the other things which they were paying attention to previously. You can spread out one spike to different things, however (if you do it at the same time), that is how your attention can be spread. You can’t do a series of smaller spikes because that confuses your mind, it is like saying, pay attention to this, then pay attention to that, and then pay attention to that. It is too confusing. It is easier to say at once, pay attention to this that and that, and then you can do it.
That explanation also explains why spikes occur at all – because it is much easier to pay a lot of attention in a short period of time then to keep jolting yourself over and over at each thing that you want to pay attention to. That way is too jarring and much less smooth.  People basically need to be focused on little things continuously, and this focus is directed by short periods of refocusing labeled here as spikes. One way in which these spikes occur is that when something is first presented it takes more energy and brain power to process it at first because it is new. It is easier to try and comprehend the entire thing at once than to comprehend it in pieces, as the latter just doesn’t make any sense. People comprehend things as wholes not as parts added up over time. The other reason these spikes occur is to initially catch your attention and hold it at a high level on something. That is, in order to go from a state of inactivity to a state of activity, you cannot just go up to the level of activity, but you need to motivate yourself to get there by having a spike (this spike is also the initial processing of the new object/event and occurs because of that as well).
In order to get someone’s attention they can’t just lazily look at you like they are looking at everything else, but they need pay sharp attention to you for the first instant (this is the initial “grabbing” talked about). Otherwise people would be paying attention to anything and everything at the same time. There has to be a way of separating out what it is that is in someone’s attention field. That method of separating is by the use of the spikes.
Spikes work for emotional things and feeling as well as for thought. That is things that are emotional occur in the same spike pattern, as well as things you feel (feelings). Another way to note this would be that your attention is only focused on things that change (things that change, the change usually occurring in spike form). It might be that something grabs your attention a little, and you only put a spike in after it initially grabs your attention a little to then pay full attention to it. Lots of time something happens, like a loud noise, that you only process after it occurred, or slightly after it occurred. So there might be a delay in when you process it, or spike it, or you might not spike it at all. You might also not need to spike something if a similar spike occurred with a similar thing previously.
How This Chapter shows how Intelligence is intertwined with Emotion:
- Someone’s attention determines what they see and figure out about the world, if someone is paying more attention then they are probably going to realize more things, or notice more things visually and intellectually. Since attention varies based on emotion, your intellect is going to vary based on your emotions. If you are emotionally interested in things then it might make you pay more attention to them and then you might realize more about those things. If something causes more of an emotional impact (or more of a spike) you might retain understanding it longer (memory is also a part of intellect) or it could increase your emotional intelligence about that thing.
- Everything that is processed follows the sequence of thought to emotion to feeling – that shows how everything in the world is real, and these real things all cause feelings, you recognize what it is (a thought) and then you feel that thought, your emotional processing of your thoughts is part of your thoughts themselves – this is obvious with emotional spikes because when you feel something strongly that strong feeling clearly aids in you understanding things about what it is you are feeling.
- People also only comprehend things in their entirety, because if it isn’t completely understood then you cannot verbalize it and make a thought process of it, therefore things that aren’t completely understood or verbal are going to be emotional and you are going to “feel” them, not think them.
References
Meyer. D.E.. & Schvaneveldt. R.W. (1971). Facilitation in recognizing paths of words: Evidence of a dependence between retrieval operations. Journal of Experimental Psychology, 90, 227-234.
Sperling. G. (1960). The information available in brief visual presentations. Psychological Monographs, 74, (Whole No.498).


9.12: Style Exercise- Voice
The de copia exercise is useful in showing how style—the third canon of rhetoric (invention, arrangement, style, memory, and delivery)—has a major impact on one’s writing. Paragraphs and essays that feature combined and varied sentences often shine the most.
For this exercise, I would like for you to try to transform your own writing to mimic another’s voice. This type of exercise is designed to help make you think about the choices a writer makes in designing his or her writing style.
You’ll complete four steps:
- Write a brief one-paragraph story that describes a key quality of yours to someone not in our class.
- Read the some sample passages and note their distinct writing styles. These are in very different genres, of course, but that’s part of the fun.
- Mimic one of those writing styles to re-tell your story. You can choose a different “audience” for your description if you’d like.
- Answer the questions : What choices did you make in re-designing your story? What obstacles did you face? How would you characterize your voice vs. the one you mimicked?


11.12: Aquifers
I hope you appreciate my spending an hour in the blazing sun to dig this hole at the beach. It is a great way to illustrate the concept of how, below a certain depth, the ground, if it is permeable enough to hold water, is saturated with water. The upper surface of this zone of saturation is called the water table. The saturated zone beneath the water table is called an aquifer, and aquifers are huge storehouses of water. What you are looking at in this picture is a “well” that exposes the water table, with an aquifer beneath it. Of course, I am cheating here, as at the beach, the level of the water table is always at the same level as the ocean, which is just below the surface of the beach.
Groundwater is one of our most valuable resource—even though you probably never see it or even realize it is there. As you may have read, most of the void spaces in the rocks below the water table are filled with water. But rocks have different porosity and permeability characteristics, which means that water does not move around the same way in all rocks below ground.
When a water-bearing rock readily transmits water to wells and springs, it is called an aquifer. Wells can be drilled into the aquifers and water can be pumped out. Precipitation eventually adds water (recharge) into the porous rock of the aquifer. The rate of recharge is not the same for all aquifers, though, and that must be considered when pumping water from a well. Pumping too much water too fast draws down the water in the aquifer and eventually causes a well to yield less and less water and even run dry. In fact, pumping your well too fast can even cause your neighbor’s well to run dry if you both are pumping from the same aquifer.
In the diagram below, you can see how the ground below the water table (the blue area) is saturated with water. The “unsaturated zone” above the water table (the greenish area) still contains water (after all, plants’ roots live in this area), but it is not totally saturated with water. You can see this in the two drawings at the bottom of the diagram, which show a close-up of how water is stored in between underground rock particles.
Figure 2.
Sometimes the porous rock layers become tilted in the earth. There might be a confining layer of less porous rock both above and below the porous layer. This is an example of a confined aquifer. In this case, the rocks surrounding the aquifer confines the pressure in the porous rock and its water. If a well is drilled into this “pressurized” aquifer, the internal pressure might (depending on the ability of the rock to transport water) be enough to push the water up the well and up to the surface without the aid of a pump, sometimes completely out of the well. This type of well is called artesian. The pressure of water from an artesian well can be quite dramatic.
A relationship does not necessarily exist between the water-bearing capacity of rocks and the depth at which they are found. A very dense granite that will yield little or no water to a well may be exposed at the land surface. Conversely, a porous sandstone, such as the Dakota Sandstone mentioned previously, may lie hundreds or thousands of feet below the land surface and may yield hundreds of gallons per minute of water. Rocks that yield freshwater have been found at depths of more than 6,000 feet, and salty water has come from oil wells at depths of more than 30,000 feet. On the average, however, the porosity and permeability of rocks decrease as their depth below land surface increases; the pores and cracks in rocks at great depths are closed or greatly reduced in size because of the weight of overlying rocks.
WATER MOVEMENT IN AQUIFERS
Water movement in aquifers is highly dependent of the permeability of the aquifer material. Permeable material contains interconnected cracks or spaces that are both numerous enough and large enough to allow water to move freely. In some permeable materials groundwater may move several metres in a day; in other places, it moves only a few centimeters in a century. Groundwater moves very slowly through relatively impermeable materials such as clay and shale.
After entering an aquifer, water moves slowly toward lower lying places and eventually is discharged from the aquifer from springs, seeps into streams, or is withdrawn from the ground by wells. Groundwater in aquifers between layers of poorly permeable rock, such as clay or shale, may be confined under pressure. If such a confined aquifer is tapped by a well, water will rise above the top of the aquifer and may even flow from the well onto the land surface. Water confined in this way is said to be under artesian pressure, and the aquifer is called an artesian aquifer.
VISUALIZING ARTESIAN PRESSURE
Here’s a little experiment to show you how artesian pressure works. Fill a plastic sandwich baggie with water, put a straw in through the opening, tape the opening around the straw closed, do not point the straw towards your teacher or parents, and then squeeze the baggie. Artesian water is pushed out through the straw.
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Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


7.2: The Bohr Model
- Describe the Bohr model of the hydrogen atom
- Use the Rydberg equation to calculate energies of light emitted or absorbed by hydrogen atoms
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model, since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus about which a single electron moves. This classical mechanics description of the atom is incomplete, however, since an electron moving in an elliptical orbit would be accelerating (by changing direction) and, according to classical electromagnetism, it should continuously emit electromagnetic radiation. This loss in orbital energy should result in the electron’s orbit getting continually smaller until it spirals into the nucleus, implying that atoms are inherently unstable.
In 1913, Niels Bohr attempted to resolve the atomic paradox by ignoring classical electromagnetism’s prediction that the orbiting electron in hydrogen would continuously emit light. Instead, he incorporated into the classical mechanics description of the atom Planck’s ideas of quantization and Einstein’s finding that light consists of photons whose energy is proportional to their frequency. Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation (the stationary state hypothesis), but it would emit or absorb a photon if it moved to a different orbit. This model leads directly to the Rydberg equation discussed in section 7.1. In this equation, h is Planck’s constant (6.62607015 x 10 -34 J sec), with \(n=1,2,3, ...\), \(k\) is a constant comprising fundamental constants such as the electron mass and charge, \(k\) has a value of \(2.179 \times 10^{–18}\; J\).
\[ \dfrac{1}{\lambda}=\dfrac{k}{hc} \left(\dfrac{1}{n^2_1}−\dfrac{1}{n_2^2}\right) ]
The lowest few energy levels are shown in Figure \(\PageIndex{1}\). One of the fundamental laws of physics is that matter is most stable with the lowest possible energy. Thus, the electron in a hydrogen atom usually moves in the \(n = 1\) orbit, the orbit in which it has the lowest energy. When the electron is in this lowest energy orbit, the atom is said to be in its ground electronic state (or simply ground state). If the atom receives energy from an outside source, it is possible for the electron to move to an orbit with a higher \(n\) value and the atom is now in an excited electronic state (or simply an excited state) with a higher energy. When an electron transitions from an excited state (higher energy orbit) to a less excited state, or ground state, the difference in energy is emitted as a photon. Similarly, if a photon is absorbed by an atom, the energy of the photon moves an electron from a lower energy orbit up to a more excited one.
We can relate the energy of electrons in atoms to what we learned previously about energy. The law of conservation of energy says that we can neither create nor destroy energy. Thus, if a certain amount of external energy is required to excite an electron from one energy level to another, that same amount of energy will be liberated when the electron returns to its initial state (Figure \(\PageIndex{2}\)). In effect, an atom can “store” energy by using it to promote an electron to a state with a higher energy and release it when the electron returns to a lower state. The energy can be released as one quantum of energy, as the electron returns to its ground state (say, from \(n = 5\) to \(n = 1\)), or it can be released as two or more smaller quanta as the electron falls to an intermediate state, then to the ground state (say, from \(n = 5\) to \(n = 4\), emitting one quantum, then to \(n = 1\), emitting a second quantum).
With three extremely puzzling paradoxes now solved (blackbody radiation, the photoelectric effect, and the hydrogen atom), and all involving Planck’s constant in a fundamental manner, it became clear to most physicists at that time that the classical theories that worked so well in the macroscopic world were fundamentally flawed and could not be extended down into the microscopic domain of atoms and molecules. Unfortunately, despite Bohr’s remarkable achievement in deriving a theoretical expression for the Rydberg constant, he was unable to extend his theory to the next simplest atom, He, which only has two electrons. Bohr’s model was severely flawed, since it was still based on the classical mechanics notion of precise orbits, a concept that was later found to be untenable in the microscopic domain, when a proper model of quantum mechanics was developed to supersede classical mechanics.
What is the energy (in joules) and the wavelength (in meters) of the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n = 4 to the orbit with n = 6? In what part of the electromagnetic spectrum do we find this radiation?
Solution
In this case, the electron starts out with \(n = 4\), so \(n_1 = 4\). It comes to rest in the \(n = 6\) orbit, so \(n_2 = 6\). The difference in energy between the two states is given by this expression:
\[ΔE=E_1−E_2=2.179 \times 10^{−18}\left(\dfrac{1}{n^2_1}−\dfrac{1}{n_2^2}\right)\]
\[ΔE=2.179 \times 10^{−18} \left(\dfrac{1}{4^2}−\dfrac{1}{6^2}\right)\; J\]
\[ΔE=2.179 \times 10^{−18} \left(\dfrac{1}{16}−\dfrac{1}{36}\right)\;J\]
\[ΔE=7.566 \times 10^{−20}\;J\]
This energy difference is positive , indicating a photon enters the system (is absorbed) to excite the electron from the n = 4 orbit up to the \(n = 6\) orbit. The wavelength of a photon with this energy is found by the expression \(E=hc \lambda\). Rearrangement gives:
\[ \lambda=\dfrac{hc}{E}\]
From the figure of electromagnetic radiation, we can see that this wavelength is found in the infrared portion of the electromagnetic spectrum.
What is the wavelength in meters and the energy in Joules of the photon produced when an electron falls from the \(n = 5\) to the \(n = 3\) level in a H atom.
- Answer
-
\(6.837 \times 10^{−7}\; m\) and \(2.90 \times 10^{–19}\; J\)
Bohr’s model of the hydrogen atom provides insight into the behavior of matter at the microscopic level, but it is does not account for electron–electron interactions in atoms with more than one electron. It does introduce several important features of all models used to describe the distribution of electrons in an atom. These features include the following:
- The energies of electrons (energy levels) in an atom are quantized, described by quantum numbers: integer numbers having only specific allowed value and used to characterize the arrangement of electrons in an atom.
- An electron’s energy increases with increasing distance from the nucleus.
- The discrete energies (lines) in the spectra of the elements result from quantized electronic energies.
Of these features, the most important is the postulate of quantized energy levels for an electron in an atom. As a consequence, the model laid the foundation for the quantum mechanical model of the atom. Bohr won a Nobel Prize in Physics for his contributions to our understanding of the structure of atoms and how that is related to line spectra emissions.
Summary
Bohr incorporated Planck’s and Einstein’s quantization ideas into a model of the hydrogen atom that resolved the paradox of atom stability and discrete spectra. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon. To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.
Glossary
- Bohr’s model of the hydrogen atom
- structural model in which an electron moves around the nucleus only in circular orbits, each with a specific allowed radius; the orbiting electron does not normally emit electromagnetic radiation, but does so when changing from one orbit to another.
- excited state
- state having an energy greater than the ground-state energy
- ground state
- state in which the electrons in an atom, ion, or molecule have the lowest energy possible
- quantum number
- integer number having only specific allowed values and used to characterize the arrangement of electrons in an atom
Contributors and Attributions
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


13.2: What Is Industrial and Organizational Psychology?
Learning Objectives
- Understand the scope of study in the field of industrial and organizational psychology
- Describe the history of industrial and organizational psychology
In 2012, people who worked in the United States spent an average of \(56.4\) hours per week working (Bureau of Labor Statistics—U.S. Department of Labor, 2013). Sleeping was the only other activity they spent more time on with an average of \(61.2\) hours per week. The workday is a significant portion of workers’ time and energy. It impacts their lives and their family’s lives in positive and negative physical and psychological ways. Industrial and organizational (I-O) psychology is a branch of psychology that studies how human behavior and psychology affect work and how they are affected by work.
Industrial and organizational psychologists work in four main contexts: academia, government, consulting firms, and business. Most I-O psychologists have a master’s or doctorate degree. The field of I-O psychology can be divided into three broad areas (See figure \(\PageIndex{1}\) and figure \(\PageIndex{2}\)): industrial, organizational, and human factors. Industrial psychology is concerned with describing job requirements and assessing individuals for their ability to meet those requirements. In addition, once employees are hired, industrial psychology studies and develops ways to train, evaluate, and respond to those evaluations. As a consequence of its concern for candidate characteristics, industrial psychology must also consider issues of legality regarding discrimination in hiring. Organizational psychology is a discipline interested in how the relationships among employees affect those employees and the performance of a business. This includes studying worker satisfaction, motivation, and commitment. This field also studies management, leadership, and organizational culture, as well as how an organization’s structures, management and leadership styles, social norms, and role expectations affect individual behavior. As a result of its interest in worker wellbeing and relationships, organizational psychology also considers the subjects of harassment, including sexual harassment, and workplace violence. Human factors psychology is the study of how workers interact with the tools of work and how to design those tools to optimize workers’ productivity, safety, and health. These studies can involve interactions as straightforward as the fit of a desk, chair, and computer to a human having to sit on the chair at the desk using the computer for several hours each day. They can also include the examination of how humans interact with complex displays and their ability to interpret them accurately and quickly. In Europe, this field is referred to as ergonomics.
The Historical Development of Industrial and Organizational Psychology
Industrial and organizational psychology had its origins in the early \(20^{th}\) century. Several influential early psychologists studied issues that today would be categorized as industrial psychology: James Cattell (1860–1944) at Columbia, Hugo Münsterberg (1863–1916) at Harvard, Walter Dill Scott (1869–1955) at Northwestern, Robert Yerkes (1876–1956) and Walter Bingham (1880–1952) at Dartmouth, and Lillian Gilbreth (1878–1972) at Purdue. Cattell, Münsterberg, and Scott had been students of Wilhelm Wundt, the father of experimental psychology. Some of these researchers had been involved in work in the area of industrial psychology before World War I. Cattell’s contribution to industrial psychology is largely reflected in his founding of a psychological consulting company, which is still operating today called the Psychological Corporation, and in the accomplishments of students at Columbia in the area of industrial psychology. In 1913, Münsterberg published Psychology and Industrial Efficiency , which covered topics such as employee selection, employee training, and effective advertising.
Scott was one of the first psychologists to apply psychology to advertising, management, and personnel selection. In 1903, Scott published two books: The Theory of Advertising and Psychology of Advertising . They are the first books to describe the use of psychology in the business world. By 1911 he published two more books, Influencing Men in Business and Increasing Human Efficiency in Business . In 1916 a newly formed division in the Carnegie Institute of Technology hired Scott to conduct applied research on employee selection (Katzell & Austin, 1992).
The focus of all this research was in what we now know as industrial psychology; it was only later in the century that the field of organizational psychology developed as an experimental science (Katzell & Austin, 1992). In addition to their academic positions, these researchers also worked directly for businesses as consultants.
The involvement of the United States in World War I in April 1917 catalyzed the participation in the military effort of psychologists working in this area. At that time Yerkes was the president of the 25-year-old American Psychological Association (APA) . The APA is a professional association in the United States for clinical and research psychologists. Today the APA performs a number of functions including holding conferences, accrediting university degree programs, and publishing scientific journals. Yerkes organized a group under the Surgeon General’s Office (SGO) that developed methods for screening and selecting enlisted men. They developed the Army Alpha test to measure mental abilities. The Army Beta test was a non-verbal form of the test that was administered to illiterate and non-English-speaking draftees. Scott and Bingham organized a group under the Adjutant General’s Office (AGO) with the goal to develop selection methods for officers. They created a catalogue of occupational needs for the Army, essentially a job-description system and a system of performance ratings and occupational skill tests for officers (Katzell & Austin, 1992).
After the war, work on personnel selection continued. For example, Millicent Pond, who received a PhD from Yale University, worked at several businesses and was director of employment test research at Scoville Manufacturing Company. She researched the selection of factory workers, comparing the results of pre-employment tests with various indicators of job performance. These studies were published in a series of research articles in the Journal of Personnel Research in the late 1920s (Vinchur & Koppes, 2014).
From 1929 to 1932 Elton Mayo (1880–1949) and his colleagues began a series of studies at a plant near Chicago, Western Electric’s Hawthorne Works (See figure \(\PageIndex{3}\)). This long-term project took industrial psychology beyond just employee selection and placement to a study of more complex problems of interpersonal relations, motivation, and organizational dynamics. These studies mark the origin of organizational psychology. They began as research into the effects of the physical work environment (e.g., level of lighting in a factory), but the researchers found that the psychological and social factors in the factory were of more interest than the physical factors. These studies also examined how human interaction factors, such as supervisorial style, enhanced or decreased productivity.
Analysis of the findings by later researchers led to the term the Hawthorne effect , which describes the increase in performance of individuals who are noticed, watched, and paid attention to by researchers or supervisors (See figure \(\PageIndex{4}\)). What the original researchers found was that any change in a variable, such as lighting levels, led to an improvement in productivity; this was true even when the change was negative, such as a return to poor lighting. The effect faded when the attention faded (Roethlisberg & Dickson, 1939). The Hawthorne-effect concept endures today as an important experimental consideration in many fields and a factor that has to be controlled for in an experiment. In other words, an experimental treatment of some kind may produce an effect simply because it involves greater attention of the researchers on the participants (McCarney et al., 2007).
In the 1930s, researchers began to study employees’ feelings about their jobs. Kurt Lewin also conducted research on the effects of various leadership styles, team structure, and team dynamics (Katzell & Austin, 1992). Lewin is considered the founder of social psychology and much of his work and that of his students produced results that had important influences in organizational psychology. Lewin and his students’ research included an important early study that used children to study the effect of leadership style on aggression, group dynamics, and satisfaction (Lewin, Lippitt, & White, 1939). Lewin was also responsible for coining the term group dynamics , and he was involved in studies of group interactions, cooperation, competition, and communication that bear on organizational psychology.
Parallel to these studies in industrial and organizational psychology, the field of human factors psychology was also developing. Frederick Taylor was an engineer who saw that if one could redesign the workplace there would be an increase in both output for the company and wages for the workers. In 1911 he put forward his theory in a book titled, The Principles of Scientific Management (See figure \(\PageIndex{5}\)). His book examines management styles, personnel selection and training, as well as the work itself, using time and motion studies.
One of the examples of Taylor’s theory in action involved workers handling heavy iron ingots. Taylor showed that the workers could be more productive by taking work rests. This method of rest increased worker productivity from \(12.5\) to \(47.0\) tons moved per day with less reported fatigue as well as increased wages for the workers who were paid by the ton. At the same time, the company’s cost was reduced from \(9.2\) cents to \(3.9\) cents per ton. Despite these increases in productivity, Taylor’s theory received a great deal of criticism at the time because it was believed that it would exploit workers and reduce the number of workers needed. Also controversial was the underlying concept that only a manager could determine the most efficient method of working, and that while at work, a worker was incapable of this. Taylor’s theory was underpinned by the notion that a worker was fundamentally lazy and the goal of Taylor’s scientific management approach was to maximize productivity without much concern for worker well-being. His approach was criticized by unions and those sympathetic to workers (Van De Water, 1997).
Gilbreth was another influential I-O psychologist who strove to find ways to increase productivity (See figure \(\PageIndex{6}\)). Using time and motion studies, Gilbreth and her husband, Frank, worked to make workers more efficient by reducing the number of motions required to perform a task. She not only applied these methods to industry but also to the home, office, shops, and other areas. She investigated employee fatigue and time management stress and found many employees were motivated by money and job satisfaction. In 1914, Gilbreth wrote the book title, The Psychology of Management: The Function of the Mind in Determining, Teaching, and Installing Methods of Least Waste , and she is known as the mother of modern management. Some of Gilbreth’s contributions are still in use today: you can thank her for the idea to put shelves inside on refrigerator doors, and she also came up with the concept of using a foot pedal to operate the lid of trash can (Gilbreth, 1914, 1998; Koppes, 1997; Lancaster, 2004). Gilbreth was the first woman to join the American Society of Mechanical Engineers in 1926, and in 1966 she was awarded the Hoover Medal of the American Society of Civil Engineers.
Taylor and Gilbreth’s work improved productivity, but these innovations also improved the fit between technology and the human using it. The study of machine–human fit is known as ergonomics or human factors psychology.
From WWII to Today
World War II also drove the expansion of industrial psychology. Bingham was hired as the chief psychologist for the War Department (now the Department of Defense) and developed new systems for job selection, classification, training, ad performance review, plus methods for team development, morale change, and attitude change (Katzell & Austin, 1992). Other countries, such as Canada and the United Kingdom, likewise saw growth in I-O psychology during World War II (McMillan, Stevens, & Kelloway, 2009). In the years after the war, both industrial psychology and organizational psychology became areas of significant research effort. Concerns about the fairness of employment tests arose, and the ethnic and gender biases in various tests were evaluated with mixed results. In addition, a great deal of research went into studying job satisfaction and employee motivation (Katzell & Austin, 1992). Today, I-O psychology is a diverse and deep field of research and practice, as you will learn about in the rest of this chapter. The Society for Industrial and Organizational Psychology (SIOP) , a division of the APA, lists \(8,000\) members (SIOP, 2014) and the Bureau of Labor Statistics—U.S. Department of Labor (2013) has projected this profession will have the greatest growth of all job classifications in the \(20\) years following 2012. On average, a person with a master’s degree in industrial-organizational psychology will earn over \(\$80,000\) a year, while someone with a doctorate will earn over \(\$110,000\) a year (Khanna, Medsker, & Ginter, 2012).
Summary
The field of I-O psychology had its birth in industrial psychology and the use of psychological concepts to aid in personnel selection. However, with research such as the Hawthorne study, it was found that productivity was affected more by human interaction and not physical factors; the field of industrial psychology expanded to include organizational psychology. Both WWI and WWII had a strong influence on the development of an expansion of industrial psychology in the United States and elsewhere: The tasks the psychologists were assigned led to development of tests and research in how the psychological concepts could assist industry and other areas. This movement aided in expanding industrial psychology to include organizational psychology.
Glossary
- Hawthorne effect
- increase in performance of individuals who are noticed, watched, and paid attention to by researchers or supervisors
- human factors psychology
- branch of psychology that studies how workers interact with the tools of work and how to design those tools to optimize workers’ productivity, safety, and health
- industrial and organizational (I-O) psychology
- field in psychology that applies scientific principles to the study of work and the workplace
- industrial psychology
- branch of psychology that studies job characteristics, applicant characteristics, and how to match them; also studies employee training and performance appraisal
- organizational psychology
- branch of psychology that studies the interactions between people working in organizations and the effects of those interactions on productivity
Contributors and Attributions
-
Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


1.15: Organizing Files and Folders
Learning Objectives
- Organize files and folders.
Finding a Specific Folder or File: File Paths
When looking for a specific folder or file, it is helpful to follow the file path . The file path tells you what folders to click on to get to the file. Read it left to right to show what folders to click on to get to the file; read it right to left to show which folders are nested in each folder.
For example:
C:\Users\Sierra Rowan\Documents\Projects\suppliers
This file path means that the file is in the suppliers folder, which is in the Projects folder, which is in the Documents folder, which is in the Sierra Rowan username folder, which is in the Users folder, which is on the C drive of the computer.
Note that the backslash is another shorthand format you might see in instructions to indicate which folder is being discussed. (For example, “Go to the Documents\Office Templates folder”)
Traveling the File Path
Rather than remembering the file path for a specific file, you can use the toolbar at the top of File Explorer or the Properties window.
Toolbar Method
For example, the screenshot below shows a folder in Windows 7 called New folder. The file path for this folder is C:\Users\user\Documents\New folder. In the screenshot below, the user could click Documents to go up one folder to the Documents folder, and the small double-arrow on the left to go up to higher folders such as user.
Clicking the blank space to the right of the folder name will reveal the entire file path, which can be copied and pasted elsewhere.
Selecting and Moving Files
There are several ways to move files:
- Click and drag the file into a folder.
- Click a file, cut using Ctrl+X, then paste into the new folder using Ctrl+V
-
Click a file, copy using Ctrl+C, then paste into the new folder using Ctrl+V (leaves the original file where it is)
- Note that the copies are not connected; edits made to one copy will not be reflected in the other copy.
- Right-click a file, select either Copy or Cut in the dialog menu, then right-click in the folder and select Paste.
Moving Multiple Files
There are a few different ways to select multiple files (which we’ll discuss below). Once you’ve selected multiple files, anything you do to a single file will be done to all selected files. (For example, clicking and dragging will move all selected files, hitting Ctrl+C will copy all selected files, etc.)
You can select multiple files at once using the following shortcuts: Hold down Ctrl while clicking to select multiple files. Hold down Shift while clicking to select two files and all the files between them. Press Ctrl+A to select all files. (Note that when using Ctrl+A, you can use Ctrl+Click to deselect files. You’ll want to deselect the destination folder, since a folder cannot be in itself.)
Contributors and Attributions
- Organizing Files and Folders. Authored by : Lumen Learning. License : CC BY: Attribution
- Matrioshka. Authored by : Nikita Kozin. Located at : https://thenounproject.com/term/matrioshka/330268/ . License : CC BY: Attribution
- Matrioshka. Authored by : Nikita Kozin. Located at : https://thenounproject.com/kozinn/collection/welcome-to-russia/?i=330264 . License : CC BY: Attribution


2.6.1: Applications – Leontief Models (Exercises)
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SECTION 2.6 PROBLEM SET: APPLICATIONS - LEONTIEF MODELS
1) Solve the following homogeneous system.
\begin{aligned}
x+y+z &=0 \\
3 x+2 y+z &=0 \\
4 x+3 y+2 z &=0
\end{aligned}
2) Solve the following homogeneous system.
\begin{aligned}
x-y-z&=0 \\
x-3 y+2 z&=0 \\
2 x-4 y+z&=0
\end{aligned}
3) Chris and Ed decide to help each other by doing repairs on each others houses. Chris is a carpenter, and Ed is an electrician. Chris does carpentry work on his house as well as on Ed's house. Similarly, Ed does electrical repairs on his house and on Chris' house.  On the other hand Ed spent half of his time on his house and half on Chris's house. If they originally agreed that each should get about a $1000 for their work, how much money should each get for their work?
4) Chris, Ed, and Paul decide to help each other by doing repairs on each others houses. Chris is a carpenter, Ed is an electrician, and Paul is a plumber. Each does work on his own house as well as on the others houses.  Ed spent half of his time on his own house, 30% on Chris' house, and remaining on Paul's house. Paul spent 40% of the time on his own house, 40% on Chris' house, and 20% on Ed's house. If they originally agreed that each should get about a $1000 for their work, how much money should each get for their work?
SECTION 2.6 PROBLEM SET: APPLICATIONS - LEONTIEF MODELS
5) Given the internal consumption matrix \(A\), and the external demand matrix \(D\) as follows.
\[A=\left[\begin{array}{lll}
.30 & .20 & .10 \\
.20 & .10 & .30 \\
.10 & .20 & .30
\end{array}\right] \quad D=\left[\begin{array}{l}
100 \\
150 \\
200
\end{array}\right] \nonumber \]
Solve the system using the open model: \(X = AX + D\) or \(X = (I - A)^{-1}D\)
6) Given the internal consumption matrix \(A\), and the external demand matrix \(D\) as follows.
\[A=\left[\begin{array}{lll}
.05 & .10 & .10 \\
.10 & .15 & .05 \\
.05 & .20 & .20
\end{array}\right] \quad D=\left[\begin{array}{c}
50 \\
100 \\
80
\end{array}\right] \nonumber \]
Solve the system using the open model: \(X = AX + D\) or \(X = (I - A)^{-1}D\)
7) An economy has two industries, farming and building. For every $1 of food produced, the farmer uses $.20 and the builder uses $.15. For every $1 worth of building, the builder uses $.25 and the farmer uses $.20. If the external demand for food is $100,000, and for building $200,000, what should be the total production for each industry in dollars?
SECTION 2.6 PROBLEM SET: APPLICATIONS - LEONTIEF MODELS
8) An economy has three industries, farming, building, and clothing. For every $1 of food produced, the farmer uses $.20, the builder uses $.15, and the tailor $.05. For every $1 worth of building, the builder uses $.25, the farmer uses $.20, and the tailor $.10. For every $1 worth of clothing, the tailor uses $.10, the builder uses $.20, the farmer uses $.15. If the external demand for food is $100 million, for building $200 million, and for clothing $300 million, what should be the total production for each in dollars?
9) Suppose an economy consists of three industries F, C, and T. The following table gives information about the internal use of each industry's production and external demand in dollars.
| F | C | T | Demand | Total | |
| F | 30 | 10 | 20 | 40 | 100 |
| C | 20 | 30 | 20 | 50 | 120 |
| T | 10 | 10 | 30 | 60 | 110 |
Find the proportion of the amounts consumed by each of the industries; that is, find the matrix \(A\).
10) If in problem 9, the consumer demand for F, C, and T becomes 60, 80, and 100, respectively, find the total output and the internal use by each industry to meet that demand.


11.1: Fields of Force
Cutting-edge science readily infiltrates popular culture, though sometimes in garbled form. The Newtonian imagination populated the universe mostly with that nice solid stuff called matter, which was made of little hard balls called atoms. In the early twentieth century, consumers of pulp fiction and popularized science began to hear of a new image of the universe, full of x-rays, N-rays, and Hertzian waves. What they were beginning to soak up through their skins was a drastic revision of Newton's concept of a universe made of chunks of matter which happened to interact via forces. In the newly emerging picture, the universe was made of force, or, to be more technically accurate, of ripples in universal fields of force. Unlike the average reader of Cosmic Stories in 1941, you now possess enough technical background to understand what a “force field” really is.
10.1.1 Why fields?
Time delays in forces exerted at a distance
What convinced physicists that they needed this new concept of a field of force? Although we have been dealing mostly with electrical forces, let's start with a magnetic example. (In fact the main reason I've delayed a detailed discussion of magnetism for so long is that mathematical calculations of magnetic effects are handled much more easily with the concept of a field of force.) First a little background leading up to our example.
A bar magnet, a , has an axis about which many of the electrons' orbits are oriented. The earth itself is also a magnet, although not a bar-shaped one.
The interaction between the earth-magnet and the bar magnet, b , makes them want to line up their axes in opposing directions (in other words such that their electrons rotate in parallel planes, but with one set rotating clockwise and the other counterclockwise as seen looking along the axes).
On a smaller scale, any two bar magnets placed near each other will try to align themselves head-to-tail, c .
Now we get to the relevant example. It is clear that two people separated by a paper-thin wall could use a pair of bar magnets to signal to each other. Each person would feel her own magnet trying to twist around in response to any rotation performed by the other person's magnet. The practical range of communication would be very short for this setup, but a sensitive electrical apparatus could pick up magnetic signals from much farther away. In fact, this is not so different from what a radio does: the electrons racing up and down the transmitting antenna create forces on the electrons in the distant receiving antenna. (Both magnetic and electric forces are involved in real radio signals, but we don't need to worry about that yet.)
A question now naturally arises as to whether there is any time delay in this kind of communication via magnetic (and electric) forces. Newton would have thought not, since he conceived of physics in terms of instantaneous action at a distance. We now know, however, that there is such a time delay. If you make a long-distance phone call that is routed through a communications satellite, you should easily be able to detect a delay of about half a second over the signal's round trip of 50,000 miles. Modern measurements have shown that electric, magnetic, and gravitational forces all travel at the speed of light, \(3\times10^8\) m/s. (In fact, we will soon discuss how light itself is made of electricity and magnetism.)
If it takes some time for forces to be transmitted through space, then apparently there is some thing that travels through space. The fact that the phenomenon travels outward at the same speed in all directions strongly evokes wave metaphors such as ripples on a pond.
More evidence that fields of force are real: they carry energy.
The smoking-gun argument for this strange notion of traveling force ripples comes from the fact that they carry energy.
First suppose that the person holding the bar magnet on the right decides to reverse hers, resulting in configuration d . She had to do mechanical work to twist it, and if she releases the magnet, energy will be released as it flips back to c . She has apparently stored energy by going from c to d . So far everything is easily explained without the concept of a field of force.
But now imagine that the two people start in position c and then simultaneously flip their magnets extremely quickly to position e , keeping them lined up with each other the whole time. Imagine, for the sake of argument, that they can do this so quickly that each magnet is reversed while the force signal from the other is still in transit. (For a more realistic example, we'd have to have two radio antennas, not two magnets, but the magnets are easier to visualize.) During the flipping, each magnet is still feeling the forces arising from the way the other magnet used to be oriented. Even though the two magnets stay aligned during the flip, the time delay causes each person to feel resistance as she twists her magnet around. How can this be? Both of them are apparently doing mechanical work, so they must be storing magnetic energy somehow. But in the traditional Newtonian conception of matter interacting via instantaneous forces at a distance, interaction energy arises from the relative positions of objects that are interacting via forces. If the magnets never changed their orientations relative to each other, how can any magnetic energy have been stored?
The only possible answer is that the energy must have gone into the magnetic force ripples crisscrossing the space between the magnets. Fields of force apparently carry energy across space, which is strong evidence that they are real things.
This is perhaps not as radical an idea to us as it was to our ancestors. We are used to the idea that a radio transmitting antenna consumes a great deal of power, and somehow spews it out into the universe. A person working around such an antenna needs to be careful not to get too close to it, since all that energy can easily cook flesh (a painful phenomenon known as an “RF burn”).
10.1.2 The gravitational field
Given that fields of force are real, how do we define, measure, and calculate them? A fruitful metaphor will be the wind patterns experienced by a sailing ship. Wherever the ship goes, it will feel a certain amount of force from the wind, and that force will be in a certain direction. The weather is ever-changing, of course, but for now let's just imagine steady wind patterns. Definitions in physics are operational, i.e., they describe how to measure the thing being defined. The ship's captain can measure the wind's “field of force” by going to the location of interest and determining both the direction of the wind and the strength with which it is blowing. Charting all these measurements on a map leads to a depiction of the field of wind force like the one shown in the figure. This is known as the “sea of arrows” method of visualizing a field.
Now let's see how these concepts are applied to the fundamental force fields of the universe. We'll start with the gravitational field, which is the easiest to understand. As with the wind patterns, we'll start by imagining gravity as a static field, even though the existence of the tides proves that there are continual changes in the gravity field in our region of space. When the gravitational field was introduced in chapter 2 , I avoided discussing its direction explicitly, but defining it is easy enough: we simply go to the location of interest and measure the direction of the gravitational force on an object, such as a weight tied to the end of a string.
In chapter 2 , I defined the gravitational field in terms of the energy required to raise a unit mass through a unit distance. However, I'm going to give a different definition now, using an approach that will be more easily adapted to electric and magnetic fields. This approach is based on force rather than energy. We couldn't carry out the energy-based definition without dividing by the mass of the object involved, and the same is true for the force-based definition. For example, gravitational forces are weaker on the moon than on the earth, but we cannot specify the strength of gravity simply by giving a certain number of newtons. The number of newtons of gravitational force depends not just on the strength of the local gravitational field but also on the mass of the object on which we're testing gravity, our “test mass.” A boulder on the moon feels a stronger gravitational force than a pebble on the earth. We can get around this problem by defining the strength of the gravitational field as the force acting on an object, divided by the object's mass:
The gravitational field vector, \(\mathbf{g}\), at any location in space is found by placing a test mass \(m_t\) at that point. The field vector is then given by \(\mathbf{g}=\mathbf{F}/m_t\), where \(\mathbf{F}\) is the gravitational force on the test mass.
We now have three ways of representing a gravitational field. The magnitude of the gravitational field near the surface of the earth, for instance, could be written as 9.8 N/kg, 9.8 \(\text{J}/\text{kg}\cdot\text{m}\), or 9.8 \(\text{m}/\text{s}^2\). If we already had two names for it, why invent a third? The main reason is that it prepares us with the right approach for defining other fields.
The most subtle point about all this is that the gravitational field tells us about what forces would be exerted on a test mass by the earth, sun, moon, and the rest of the universe, if we inserted a test mass at the point in question. The field still exists at all the places where we didn't measure it.
| Example 1: Gravitational field of the earth |
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\(\triangleright\) What is the magnitude of the earth's gravitational field, in terms of its mass, \(M\), and the distance \(r\) from its center?
\(\triangleright\) Substituting \(|\mathbf{F}|= GMm_{t}/ r^2\) into the definition of the gravitational field, we find \(|\mathbf{g}|= GM/ r^2\). This expression could be used for the field of any spherically symmetric mass distribution, since the equation we assumed for the gravitational force would apply in any such case. |
Sources and sinks
If we make a sea-of-arrows picture of the gravitational fields surrounding the earth, g , the result is evocative of water going down a drain. For this reason, anything that creates an inward-pointing field around itself is called a sink. The earth is a gravitational sink. The term “source” can refer specifically to things that make outward fields, or it can be used as a more general term for both “outies” and “innies.” However confusing the terminology, we know that gravitational fields are only attractive, so we will never find a region of space with an outward-pointing field pattern.
Knowledge of the field is interchangeable with knowledge of its sources (at least in the case of a static, unchanging field). If aliens saw the earth's gravitational field pattern they could immediately infer the existence of the planet, and conversely if they knew the mass of the earth they could predict its influence on the surrounding gravitational field.
Superposition of indexsuperposition of fieldsindexfieldssuperposition offields
A very important fact about all fields of force is that when there is more than one source (or sink), the fields add according to the rules of vector addition. The gravitational field certainly will have this property, since it is defined in terms of the force on a test mass, and forces add like vectors. Superposition is an important characteristics of waves, so the superposition property of fields is consistent with the idea that disturbances can propagate outward as waves in a field.
| Example 2: Reduction in gravity on Io due to Jupiter's gravity |
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\(\triangleright\) The average gravitational field on Jupiter's moon Io is 1.81 N/kg. By how much is this reduced when Jupiter is directly overhead? Io's orbit has a radius of \( 4.22\times10^8\) m, and Jupiter's mass is \( 1.899\times10^{27}\) kg. \(\triangleright\) By the shell theorem, we can treat the Jupiter as if its mass was all concentrated at its center, and likewise for Io. If we visit Io and land at the point where Jupiter is overhead, we are on the same line as these two centers, so the whole problem can be treated one-dimensionally, and vector addition is just like scalar addition. Let's use positive numbers for downward fields (toward the center of Io) and negative for upward ones. Plugging the appropriate data into the expression derived in example 1 , we find that the Jupiter's contribution to the field is \(- 0.71\) N/kg. Superposition says that we can find the actual gravitational field by adding up the fields created by Io and Jupiter: \(1.81-0.71\) N/kg = 1.1 N/kg. You might think that this reduction would create some spectacular effects, and make Io an exciting tourist destination. Actually you would not detect any difference if you flew from one side of Io to the other. This is because your body and Io both experience Jupiter's gravity, so you follow the same orbital curve through the space around Jupiter. |
Gravitational waves
A source that sits still will create a static field pattern, like a steel ball sitting peacefully on a sheet of rubber. A moving source will create a spreading wave pattern in the field, like a bug thrashing on the surface of a pond. Although we have started with the gravitational field as the simplest example of a static field, stars and planets do more stately gliding than thrashing, so gravitational waves are not easy to detect. Newton's theory of gravity does not describe gravitational waves, but they are predicted by Einstein's general theory of relativity. J.H. Taylor and R.A. Hulse were awarded the Nobel Prize in 1993 for giving indirect evidence that Einstein's waves actually exist. They discovered a pair of exotic, ultra-dense stars called neutron stars orbiting one another very closely, and showed that they were losing orbital energy at the rate predicted by Einstein's theory.
A Caltech-MIT collaboration has built a pair of gravitational wave detectors called LIGO to search for more direct evidence of gravitational waves. Since they are essentially the most sensitive vibration detectors ever made, they are located in quiet rural areas, and signals will be compared between them to make sure that they were not due to passing trucks. The project began operating at full sensitivity in 2005, and is now able to detect a vibration that causes a change of \(10^{-18}\) m in the distance between the mirrors at the ends of the 4-km vacuum tunnels. This is a thousand times less than the size of an atomic nucleus! There is only enough funding to keep the detectors operating for a few more years, so the physicists can only hope that during that time, somewhere in the universe, a sufficiently violent cataclysm will occur to make a detectable gravitational wave. (More accurately, they want the wave to arrive in our solar system during that time, although it will have been produced millions of years before.)
10.1.3 The electric field
Definition
The definition of the electric field is directly analogous to, and has the same motivation as, the definition of the gravitational field:
The electric field vector, \(\mathbf{E}\), at any location in space is found by placing a test charge \(q_t\) at that point. The electric field vector is then given by \(\mathbf{E}=\mathbf{F}/q_t\), where \(\mathbf{F}\) is the electric force on the test charge.
Charges are what create electric fields. Unlike gravity, which is always attractive, electricity displays both attraction and repulsion. A positive charge is a source of electric fields, and a negative one is a sink.
The most difficult point about the definition of the electric field is that the force on a negative charge is in the opposite direction compared to the field. This follows from the definition, since dividing a vector by a negative number reverses its direction. It's as though we had some objects that fell upward instead of down.
self-check:
Find an equation for the magnitude of the field of a single point charge \(Q\).
(answer in the back of the PDF version of the book)
| Example 3: Superposition of electric fields |
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\(\triangleright\) Charges \(q\) and \(- q\) are at a distance \(b\) from each other, as shown in the figure. What is the electric field at the point P, which lies at a third corner of the square?
\(\triangleright\) The field at P is the vector sum of the fields that would have been created by the two charges independently. Let positive \(x\) be to the right and let positive \(y\) be up. Negative charges have fields that point at them, so the charge \(-q\) makes a field that points to the right, i.e., has a positive \(x\) component. Using the answer to the self-check, we have
\[\begin{align*} E_{-q,x} &= \frac{ kq}{ b^2} \\ E_{-q,y} &= 0 . \end{align*}\]
Note that if we had blindly ignored the absolute value signs and plugged in \(- q\) to the equation, we would have incorrectly concluded that the field went to the left. By the Pythagorean theorem, the positive charge is at a distance \(\sqrt{2} b\) from P, so the magnitude of its contribution to the field is \(E= kq/2 b^2\). Positive charges have fields that point away from them, so the field vector is at an angle of 135° counterclockwise from the \(x\) axis.
\[\begin{align*} E_{q,x} &= \frac{ kq}{2 b^2} \text{cos}\ 135° \\ &= -\frac{ kq}{2^\text{3/2} b^2} \\ E_{q,y} &= \frac{ kq}{2 b^2} \text{sin}\ 135° \\ &= \frac{ kq}{2^\text{3/2} b^2} \end{align*}\]
The total field is
\[\begin{align*} E_\text{x} &= \left(1-2^{-\text{3/2}}\right)\frac{ kq}{ b^2} \\ E_{y} &= \frac{ kq}{2^\text{3/2} b^2} \end{align*}\]
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Dipoles
The simplest set of sources that can occur with electricity but not with gravity is the dipole , consisting of a positive charge and a negative charge with equal magnitudes. More generally, an electric dipole can be any object with an imbalance of positive charge on one side and negative on the other.
A water molecule, l , is a dipole because the electrons tend to shift away from the hydrogen atoms and onto the oxygen atom.
Your microwave oven acts on water molecules with electric fields. Let us imagine what happens if we start with a uniform electric field, m /1, made by some external charges, and then insert a dipole, m /2, consisting of two charges connected by a rigid rod. The dipole disturbs the field pattern, but more important for our present purposes is that it experiences a torque. In this example, the positive charge feels an upward force, but the negative charge is pulled down. The result is that the dipole wants to align itself with the field, m /3. The microwave oven heats food with electrical (and magnetic) waves. The alternation of the torque causes the molecules to wiggle and increase the amount of random motion. The slightly vague definition of a dipole given above can be improved by saying that a dipole is any object that experiences a torque in an electric field.
What determines the torque on a dipole placed in an externally created field? Torque depends on the force, the distance from the axis at which the force is applied, and the angle between the force and the line from the axis to the point of application. Let a dipole consisting of charges \(+q\) and \(-q\) separated by a distance \(\ell\) be placed in an external field of magnitude \(|\mathbf{E}|\), at an angle \(\theta\) with respect to the field. The total torque on the dipole is
(Note that even though the two forces are in opposite directions, the torques do not cancel, because they are both trying to twist the dipole in the same direction.) The quantity is called the dipole moment, notated \(D\). (More complex dipoles can also be assigned a dipole moment --- they are defined as having the same dipole moment as the two-charge dipole that would experience the same torque.)
Employing a little more mathematical elegance, we can define a dipole moment vector ,
where \(\mathbf{r}_i\) is the position vector of the charge labeled by the index \(i\). We can then write the torque in terms of a vector cross product (page 281),
No matter how we notate it, the definition of the dipole moment requires that we choose point from which we measure all the position vectors of the charges. However, in the commonly encountered special case where the total charge of the object is zero, the dipole moment is the same regardless of this choice.
| Example 4: Dipole moment of a molecule of NaCl gas |
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\(\triangleright\) In a molecule of NaCl gas, the center-to-center distance between the two atoms is about 0.6 nm. Assuming that the chlorine completely steals one of the sodium's electrons, compute the magnitude of this molecule's dipole moment. \(\triangleright\) The total charge is zero, so it doesn't matter where we choose the origin of our coordinate system. For convenience, let's choose it to be at one of the atoms, so that the charge on that atom doesn't contribute to the dipole moment. The magnitude of the dipole moment is then
\[\begin{align*} D &= (6\times10^{-10}\ \text{m})( e) \\ &= (6\times10^{-10}\ \text{m})( 1.6\times10^{-19}\ \text{C}) \\ &= 1\times10^{-28}\ \text{C}\cdot\text{m} \end{align*}\]
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| Example 5: Dipole moments as vectors |
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\(\triangleright\) The horizontal and vertical spacing between the charges in the figure is \(b\). Find the dipole moment.
\(\triangleright\) Let the origin of the coordinate system be at the leftmost charge.
\[\begin{align*} \mathbf{D} &= \sum q_i \mathbf{r}_i \\ &= (q)(\text{0})+(-q)(b\hat{\mathbf{x}})+(q)(b\hat{\mathbf{x}}+b\hat{\mathbf{y}})+(-q)(2b\hat{\mathbf{x}}) \\ &= -2bq\hat{\mathbf{x}}+bq\hat{\mathbf{y}} \end{align*}\]
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Alternative definition of the electric field
The behavior of a dipole in an externally created field leads us to an alternative definition of the electric field:
The electric field vector, \(E\), at any location in space is defined by observing the torque exerted on a test dipole \(D_t\) placed there. The direction of the field is the direction in which the field tends to align a dipole (from \(-\) to +), and the field's magnitude is \(|\mathbf{E}|=\tau/D_t\sin\theta\). In other words, the field vector is the vector that satisfies the equation \(\boldsymbol{\tau} = \mathbf{D}_t\times\mathbf{E}\) for any test dipole \(\mathbf{D}_t\) placed at that point in space.
The main reason for introducing a second definition for the same concept is that the magnetic field is most easily defined using a similar approach.
Discussion Questions
◊ In the definition of the electric field, does the test charge need to be 1 coulomb? Does it need to be positive?
◊ Does a charged particle such as an electron or proton feel a force from its own electric field?
◊ Is there an electric field surrounding a wall socket that has nothing plugged into it, or a battery that is just sitting on a table?
◊ In a flashlight powered by a battery, which way do the electric fields point? What would the fields be like inside the wires? Inside the filament of the bulb?
◊ Criticize the following statement: “An electric field can be represented by a sea of arrows showing how current is flowing.”
◊ The field of a point charge, \(|\mathbf{E}|=kQ/r^2\), was derived in a self-check. How would the field pattern of a uniformly charged sphere compare with the field of a point charge?
◊ The interior of a perfect electrical conductor in equilibrium must have zero electric field, since otherwise the free charges within it would be drifting in response to the field, and it would not be in equilibrium. What about the field right at the surface of a perfect conductor? Consider the possibility of a field perpendicular to the surface or parallel to it.
◊ Compare the dipole moments of the molecules and molecular ions shown in the figure.
◊ Small pieces of paper that have not been electrically prepared in any way can be picked up with a charged object such as a charged piece of tape. In our new terminology, we could describe the tape's charge as inducing a dipole moment in the paper. Can a similar technique be used to induce not just a dipole moment but a charge?
Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.