2.4: Electric Fields and Forces
By the end of this section, you will be able to:
- Explain the purpose of the electric field concept
- Describe the properties of the electric field
- Calculate the electric force that charges exert on each other
- Determine the direction of the electric force for different source charges
Having seen the qualitative effects of charged objects on other charged objects, we would also like to be able to calculate quantities related to these effects. In this section, we will begin to define our approach to these calculations.
Defining a Field
We have seen experimentally that electric charges can have effects over a distance without contact. It is then natural to hypothesize that a physical field around a charged particle exists that can exert force on other charged particles. Mathematically, a physical field is a function that gives a value of a physical quantity at each point in space and each moment in time (see Example \(\PageIndex{1}\) and Example \(\PageIndex{2}\)).
In weather reports, a temperature field can be visualized on a map showing the temperature's value at each point on the map at a specific moment in time. Because each temperature is a number, this field is known as a scalar field .
Weather reports will also sometimes give a wind velocity field. In this case, the map shows the magnitude and direction of the wind at each point on the map at a specific moment in time. Because the wind velocity is a vector, this field is known as a vector field .
Defining the Electric Field
Because we expect the field around a charge to exert a force, which is a vector quantity, we will hypothesize that the electric field is a vector field. For simplicity, we will start by considering the source of the field to be a single point charge , which we define as an idealized particle at a single point in space at coordinates \( (x_s, y_s, z_s) \) carrying a specified source charge \( q \). Based on experimental evidence, we define the electric field at test location \( (x_t, y_t, z_t) \) away from the source charge to be
\[\vec{E} = \dfrac{1}{4 \pi \epsilon_0} \dfrac{q}{r^2}\hat{r}, \label{Efield0} \]
where \(\epsilon_0\) is the permittivity of free space (vacuum), \( r \) is the separation distance between the source charge and test location, and \( \hat{r} \) is the radial unit vector that points in the direction from the source charge to the test location. From geometry, the distance between the source charge and test location is given by
\[ r = [(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2}, \label{rdistance} \]
where \( \Delta x = x_t - x_s \), \( \Delta y = y_t - t=y_s \), \( \Delta z = z_t - z_s \) are the differences in coordinates between the test and source charges. Note that the Also, from geometry, the radial unit vector is
\[ \hat{r} = \dfrac{(\Delta x)\hat{i}+(\Delta y)\hat{j}+(\Delta z)\hat{k}}{[(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2}} \label{rhat} \]
The radial unit vector in Equation \ref{Efield0} ensures that the electric field is always directed along the line between the source charge and the test location. The numerator sets the proper direction, while the denominator ensures that the length of the unit vector is one.
The radial unit vector always points away from the source charge and toward the test location. You can remember this relation from the " rst " memory aid:
r
-hat points from
s
ource to
t
est
This is true regardless of the sign of the source charge, as Equation \ref{rhat} does not contain any charge terms.
A consequence of Equation \ref{Efield0} is that the direction of the electric field is determined by the sign of the source charge. If the source charge is positive, the electric field points in the same direction as the radial unit vector (outward). If the source charge is negative, the electric field points in the opposite direction as the radial unit vector (inward).
By convention, all electric fields \(\vec{E}\) point away from positive source charges and point toward negative source charges.
It is important to emphasize that the electric field is not constant around a point charge but instead falls off as the reciprocal of the square of the separation distance. In addition, if either the source charge's location or the test location moves, then \( r \) and \(\hat{r}\) change, and therefore, so does the electric field.
The permittivity of free space has a very important physical meaning that we will discuss in a later chapter; for now, it is simply an empirical proportionality constant. Its numerical value (to three significant figures) turns out to be
\[\epsilon_0 = 8.85 \times 10^{-12} \dfrac{\mathrm{C}^2}{\mathrm{N} \cdot \mathrm{m}^2}.\]
These units are required to give the electric field in the correct units of newtons per coulomb. For convenience, we often define the electrostatic constant (also known as Coulomb's constant) to be
\[ k = \dfrac{1}{4\pi \epsilon_0} = 8.99 \times 10^9 \dfrac{\mathrm{N} \cdot \mathrm{m}^2}{\mathrm{C}^2}.\]
A consequence of these constants being given in units of meters and coulombs is that the charge and separation distance in Equation \ref{Efield0} must also be given those same units to ensure that the force is in units of newtons.
Strictly speaking, Equation \ref{Efield0} is only valid for a point charge. However, it will still usually be a good approximation for the electric field of a uniformly charged particle at distances that are large compared to the size of the particle. Example \(\PageIndex{3}\) shows how you can calculate electric fields and forces for a problem with two point charges.
Electric Field Due to Point Charges
(a) Suppose a point charge of +5.00nC is located at Point \( P_1 \) with coordinates \( (-2.00\ \mathrm{m}, +2.00\ \mathrm{m}, 0.00\ \mathrm{m}) \). What is the electric field at Point \( P_2 \) \( (+2.00\ \mathrm{m}, +1.00\ \mathrm{m}, 0.00\ \mathrm{m}) \)?
(b) What is the strength (magnitude) of the electric field at \( (+2.00\ \mathrm{m}, +1.00\ \mathrm{m}, 0.00\ \mathrm{m}) \)?
Solution
(a) We will follow a four-step problem-solving strategy:
PLAN We have a point charge, so we plan to use Eq. \(\ref{Efield0}\) to find the electric field.
SKETCH However, before we start to calculate, it is important to make a drawing of the geometry of the problem, marking the source charge at Point \( P_1 \) and the test location at Point \( P_2 \). We can also sketch in the direction of the radial unit vector because we know it lines along the line connecting Points \( P_1 \) and \( P_2 \) and points away from the source charge and toward the test location. We will later use the sketch to check our calculations.
CALCULATE To use Eq. \(\ref{Efield0}\), we must first know the charge, separation distance, and radial unit vector. We first convert the charge to coulombs by writing \( q = 5\ \mathrm{nC} = 5 \times 10^{-9}\ \mathrm{C}\). Next, we identify the location of the source charge as \( (x_s, y_s, z_s) = (-2.00\ \mathrm{m}, +2.00\ \mathrm{m}, 0.00\ \mathrm{m}) \) and the test location as \( (x_t, y_t, z_t) = (+2.00\ \mathrm{m}, -1.00\ \mathrm{m}, 0.00\ \mathrm{m}) \). As a result,
\[ \begin{align*}
\Delta x &= x_t - x_s = +2.00\ \mathrm{m} - -2.00\ \mathrm{m} = +4.00\ \mathrm{m},\\
\Delta y &= y_t - y_s = -1.00\ \mathrm{m} - 2.00\ \mathrm{m} = -3.00\ \mathrm{m}, \\
\Delta z & = z_t - z_s = 0.00\ \mathrm{m} - 0.00\ \mathrm{m} = 0.00\ \mathrm{m},
\end{align*} \]
and therefore the separation distance is given by Equation \ref{rdistance}
\[ r = [(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2} = [(+4.00\ \mathrm{m})^2 + (-3.00\ \mathrm{m})^2 + (0.00\ \mathrm{m})^2]^{1/2} = 5.00\ \mathrm{m}. \nonumber \]
The radial unit vector is then given by Equation \ref{rhat}
\[ \hat{r} = \dfrac{(\Delta x)\hat{i}+(\Delta y)\hat{j}+(\Delta z)\hat{k}}{[(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2}}
= \dfrac{(+4.00\ \mathrm{m})\hat{i}+(-3.00\ \mathrm{m})\hat{j}+(0.00\ \mathrm{m})\hat{k}}{5.00\ \mathrm{m}}
= +0.800 \hat{i} - 0.600\hat{j}.
\nonumber \]
Observe that the radial unit vector is always dimensionless; the dimensions come from the other quantities in the problem. The electric field at the test location is then given by Eq. \(\ref{Efield0}\)
\[ \vec{E} = \dfrac{1}{4 \pi \epsilon_0} \dfrac{q}{r^2}\hat{r}
= \left(8.99 \times 10^9 \dfrac{\mathrm{N} \cdot \mathrm{m}^2}{\mathrm{C}^2}\right)
\dfrac{5.00 \times 10^{-9}\ \mathrm{C}}{(5.00\ \mathrm{m})^2}(0.800 \hat{i} - 0.600\hat{j})
=(+1.44\ \mathrm{N/C})\hat{i} +(-1.08\ \mathrm{N/C})\hat{j}
\]
CHECK The calculated electric field vector indicates that the vector points down and to the right, a result which is consistent with Fig. \(\PageIndex{3}\). It also indicates that the x-component is larger than the y-component, which is also consistent with the diagram. Finally, the units are in newtons per coulomb, as expected.
(b) The strength of the electric field is the magnitude of the electric field vector
\[|\vec{E}| = \dfrac{1}{4 \pi \epsilon_0} \dfrac{|q|}{r^2}=[(+1.44\ \mathrm{N/C})^2+(-1.08\ \mathrm{N/C})^2]^{1/2} = 1.80\ \mathrm{N/C}\]
Defining Electric Force
Experiments with electric charges have shown that if two objects each have electric charge, then they exert an electric force on each other. The electric field is useful because once we know the electric field at a test location, we can then calculate the electric force \(\vec{F}\) on a point charge \( Q \) ("test charge") placed at that test location simply by multiplying the charge and electric field together
\[\vec{F_E} = Q \vec{E}. \label{Efield1} \]
With charge in coulombs (C) and electric field in newtons per coulombs (N/C) , their product will be in newtons, as expected for force. Example \(\PageIndex{4}\) show how you can calculate electric force between two point charges.
Continuing with the scenario of Example \( \PageIndex{3}\),
(a) Suppose a second point charge of −3.00 nC is now placed at Point \( P_2 \). What is the electric force exerted on this new second charge of −3.00 nC due to the original charge of +5.00 nC?
(b) What is the electric force exerted on the original charge of +5.00 nC due to the second charge of −3.00 nC?
Solution
(a) We will follow a four-step problem-solving strategy:
PLAN Because we already know the electric field at Point \( P_2 \) and are given a second point charge, we can use Equation \ref{Efield1} to find the electric force.
SKETCH We can modify our previous diagram to show the geometry of both charges relative to each other. It is also a good idea to draw the radial unit vector and vectors in the expected directions of the electric field and electric force. Note that the radial unit vector still points in the same direction as in Fig. \(\PageIndex{3}\) because the +5 nC charge is still the source charge creating the electric field that is exerting the electric force on the −3 nC charge. The electric field vector is in the same direction as the radial unit vector because the source charge is positive. However, the direction of the electric force is in the opposite direction of the radial unit vector because we know that positive and negative charges attract.
CALCULATE The electric force is given by Equation \ref{Efield1}
\[ \vec{F_E} = Q \vec{E} = (-3.00\times 10^{-9}\ \mathrm{C})[(+1.44\ \mathrm{N/C})\hat{i} +(-1.08\ \mathrm{N/C})\hat{j}]
= (-4.31\times 10^{-7}\ \mathrm{N})\hat{i} +(3.24\times 10^{-7}\ \mathrm{N})\hat{j} \nonumber \]
Note that the test charge must be written in coulombs in Equation \ref{Efield1} to ensure the force is in newtons.
CHECK The calculated force is directed left and up, a result which is consistent with the expected attractive force.
(b) In this question, we are asked to find the electric force exerted by the second charge of −3.00 nC on the +5.00 nC charge. In other words, the charges have switched roles, so the −3.00 nC charge is now the source charge and the +5.00 nC charge is the test charge. The electric field at Point \( P_1 \) due to the −3.00 nC charge can then be calculated using the same approach as in Example \(\PageIndex{3}\).
The location of the source charge is \( (x_s, y_s, z_s) = (+2.00\ \mathrm{m}, -1.00\ \mathrm{m}, 0.00\ \mathrm{m}) \), while the test location is \( (x_t, y_t, z_t) = (-2.00\ \mathrm{m}, +2.00\ \mathrm{m}, 0.00\ \mathrm{m}) \). As a result,
\[ \begin{align*}
\Delta x &= x_t - x_s = -2.00\ \mathrm{m} - 2.00\ \mathrm{m} = -4.00\ \mathrm{m},\\
\Delta y &= y_t - y_s = 2.00\ \mathrm{m} - -1.00\ \mathrm{m} = +3.00\ \mathrm{m}, \\
\Delta z & = z_t - z_s = 0.00\ \mathrm{m} - 0.00\ \mathrm{m} = 0.00\ \mathrm{m},
\end{align*} \]
and therefore the separation distance is given by Equation \ref{rdistance}
\[ r = [(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2} = [(-4.00\ \mathrm{m})^2 + (+3.00\ \mathrm{m})^2 + (0.00\ \mathrm{m})^2]^{1/2} = 5.00\ \mathrm{m}. \nonumber \]
The radial unit vector is then given by Equation \ref{rhat}
\[ \hat{r} = \dfrac{(\Delta x)\hat{i}+(\Delta y)\hat{j}+(\Delta z)\hat{k}}{[(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2]^{1/2}}
= \dfrac{(-4.00\ \mathrm{m})\hat{i}+(3.00\ \mathrm+{m})\hat{j}+(0.00\ \mathrm{m})\hat{k}}{5.00\ \mathrm{m}}
= -0.800 \hat{i} + 0.600\hat{j}.
\nonumber \]
The electric field at the test location of Point \( P_1 \) is given by Eq. \(\ref{Efield0}\)
\[ \vec{E} = \dfrac{1}{4 \pi \epsilon_0} \dfrac{q}{r^2}\hat{r}
= \left(8.99 \times 10^9 \dfrac{\mathrm{N} \cdot \mathrm{m}^2}{\mathrm{C}^2}\right)
\dfrac{-3.00 \times 10^{-9}\ \mathrm{C}}{(5.00\ \mathrm{m})^2}(-0.800 \hat{i} + 0.600\hat{j})
=(+0.863\ \mathrm{N/C})\hat{i} +(-0.647\ \mathrm{N/C})\hat{j}
\nonumber \]
According to Equation \ref{Efield1}, the electric force on the +5 nC charge is then
\[ \vec{F_E} = Q \vec{E} = (+5.00\times 10^{-9}\ \mathrm{C})[(0.863\ \mathrm{N/C})\hat{i} +(-0.647\ \mathrm{N/C})\hat{j}]
= (+4.31\times 10^{-7}\ \mathrm{N})\hat{i} + (-3.24\times 10^{-7}\ \mathrm{N})\hat{j} \nonumber \]
We see that the force has the same magnitude as in part (a) but opposite direction. This result should be expected because we know from experiments that the positive and negative charges attract.
Open the Electric Field of Dreams applet. This applet allows you to construct an electric field and then insert one or more charged particles into the field.
Instructions:
- Open the applet and choose the appropriate emulation for your system (usually CheepJ will work).
- Click on the blue dot in the "External Field" box and then drag it in some direction to define the magnitude and direction of the electric field.
- Press the Click on the "Properties" button, and then enter the desired values of charge and mass for a particle.
- Click on the "Add" button to add the particle to the field. Is the motion of the particle make sense? Is it consistent with Eq. (\(\PageIndex{8}\))?
- Click on the "Properties" button again, and change the properties to have the opposite sign of charge. Click on the "Add" button to add this second particle.
- Observe the motion of the particles together. Does the motion of the second particle make sense? Can you see the particles interacting with each other?
Source: Electric Field of Dreams
Simulation by PhET Interactive Simulations , University of Colorado Boulder, licensed under CC-BY-4.0 (opens in new window) .
Coulomb's Law
Substituting Equation \ref{Efield0} into Equation \ref{Efield1} yields an equation that allows you to calculate the electric force between two point charges directly. This equation is usually called Coulomb's Law .
The electric force exerted by a point charge \( q_1 \) on a point charge \( q_2 \) separated by a distance \( r_{12} \) is equal to
\[ \vec{F}_{12} = \dfrac{1}{4 \pi \epsilon_0} \dfrac{q_{1} q_{2}}{r_{12}^2}\hat{r}_{12}, \label{Coulomb} \]
where \(\hat{r}_{12}\) is the radial unit vector directed from the location of charge \( q_1 \) to the location of charge \( q_2 \).
We see that the magnitude of electric force is proportional to the product of the charges and inversely proportional to the square of the separation distance between the charges. The form of Equation \ref{Coulomb} shows more clearly why the electric forces calculated in parts (a) and (b) in Example \(\PageIndex{4}\) must be equal in magnitude, because the magnitude of the force does not change if the roles of \( q_1 \) and \( q_2 \) are reversed and must be opposite in direction because \( \hat{r}_{12} = -\hat{r}_{21} \).
Observe that Coulomb's Law allows the electric forces between two charges to be repulsive or attractive. If the charges have the same sign, then their product is positive, the electric force is in the same direction as \(\hat{r}\), and the force is repulsive. If the charges have opposite signs, then their product is negative, the force is in the opposite direction of \(\hat{r}\), and the force is attractive. This idea is illustrated in Figure \(\PageIndex{5}\).
The following interactive simulation further illustrates the qualitative and quantitative properties of Coulomb's Law.
Instructions:
- Select "Macro Scale".
- Move the slider back and forth for Charge 1 to adjust its charge from negative to zero to positive. How do the forces on the charges change?
- Move the slider back and forth for Charge 2 to adjust its charge from negative to zero to positive. How do the forces on the charges change?
- Is there a scenario where the forces are ever unequal in magnitude or in the same direction?
- Move Charge 1 to the zero position, and then move the position of Charge 2. Does the inverse square law hold?
-
Bonus: Select the "Atomic Scale" button at the bottom of the screen. How do the results change at the smaller scale?
Source: Coulomb's Law
Simulation by PhET Interactive Simulations , University of Colorado Boulder, licensed under CC-BY-4.0 (opens in new window) .
Example \(\PageIndex{5}\) shows how Coulomb's Law can be applied to a familiar system of two charges, the hydrogen atom.
A hydrogen atom consists of a single proton and a single electron. The proton has a charge of \(+e\), and the electron has \(-e\). In the “ground state” of the atom, the electron orbits the proton at the most probable distance of \(5.29 \times 10^{-11}\ \mathrm{m}\) ). Calculate the electric force on the electron due to the proton.
PLAN For the purposes of this example, we are treating the electron and proton as two point particles, each with an electric charge, and we are told the distance between them; we are asked to calculate the force on the electron. We thus use Coulomb’s law (Equation \ref{Coulomb}).
SKETCH Figure \(\PageIndex{6}\) shows a diagram the hydrogen atom with the force vector marked.
CALCULATE Our two charges are \( q_1 = +e = +1.602 \times 10^{-19}\ \mathrm{C}\) and \( q_2 = -e = -1.602 \times 10^{-19}\ \mathrm{C} \), and the distance between them is given to be \(r = 5.29 \times 10^{-11}\ \mathrm{m}\).
The force on the electron from Equation \ref{Coulomb} is
\[\begin{align*}
\vec{F_E} &= \dfrac{1}{4\pi \epsilon_0}\dfrac{q_1 q_2}{r_{12}^2} \hat{r}\\[4pt]
&= \dfrac{1}{4\pi \left(8.85 \times 10^{-12} \frac{\mathrm{C}^2}{\mathrm{N} \cdot \mathrm{m}^2} \right)} \dfrac{(1.602 \times 10^{-19}\ \mathrm{C})(-1.602 \times 10^{-19}\ \mathrm{C})}{(5.29 \times 10^{-11}\ \mathrm{m})^2} \\[4pt]
&= (8.25 \times 10^{-8}\ \mathrm{N})(-\hat{r})
\end{align*}\]
Because the charges on the two particles are opposite, the force is negative (attractive); the force on the electron points radially directly toward the proton, everywhere in the electron’s orbit.
CHECK This is a three-dimensional system, so the electron (and therefore the force on it) can be anywhere in an imaginary spherical shell around the proton. In this “classical” model of the hydrogen atom, the electrostatic force on the electron points in the inward centripetal direction , thus maintaining the electron’s orbit. However, the more accurate quantum-mechanical model of hydrogen (discussed in Quantum Mechanics ) is utterly different.
If you have studied Newtonian mechanics, you will be familiar with gravitational fields as another type of fundamental physical field. Interestingly, there are parallels between electric and gravitational fields and forces, as discussed in Example \(\PageIndex{6}\).
Comparison: Gravitational Fields & Forces vs. Electric Fields & Forces
The mathematical equation for the electric field \(\vec{E}\) of a point charge (Equation \ref{Efield0}) is similar to the gravitational field \(\vec{g}\) of Earth
\[\vec{g} = -G \dfrac{M_e}{r^2}\hat{r}, \label{gfield0} \]
where \( G = 6.67 \times 10^{-11}\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2 \) is the gravitational constant, \( M_e = 5.98\times 10^{24}\ \mathrm{kg}\) is the mass of the Earth, and \( r \) is the distance away from the Earth's center, assuming the Earth is approximately spherical. You can see that the proportionality constant \(G\) plays the same role for the gravitational field \(\vec{g}\) as the electrostatic constant \(k = \frac{1}{4\pi \epsilon_0}\) does for the electric field \(\vec{E}\).
On the surface of the Earth, the distance \( r = R_e = 6.37 \times 10^6\ \mathrm{m}\) is the radius of the Earth, and Equation \ref{gfield0} reduces down to
\[\vec{g} = -G\dfrac{M_e}{R_e^2}\hat{r} = (9.81\ \mathrm{N/kg})(-\hat{r}) \ \ \ \text{(On Earth's surface only)} \nonumber \]
The factor \( 9.81\ \mathrm{N/kg}= 9.81 \mathrm{m}/\mathrm{s}^2\) is recognized as the acceleration of gravity, and the factor \(-\hat{r}\) indicates that the force is attractive and directed toward the center of the Earth, as expected.
Once we have calculated the gravitational field at some point in space due to a source mass, we can use it any time we want to calculate the resulting force on any test mass we choose to place at that test location according to
\[\vec{F_G} = M \vec{g} . \label{gfield1} \]
In fact, this is exactly what we do when we calculate the force on different masses due to gravity (i.e., weight). You can see this equation is similar in form to Equation \ref{Efield1} for the electric force, with charge replacing mass. Combining Eqs. \ref{gfield0} and \ref{gfield1} yields the equation
\[ \vec{F}_{12} = -G \dfrac{m_{1} m_{2}}{r_{12}^2} \hat{r}_{12}, \label{NewtonGravity} \]
which is Newton's Law of Universal Gravitation and, similar to Coulomb's Law, is an inverse-square law in the separation distance.
One significant difference between Coulomb's Law and Newton's Law of Universal Gravitation is that charge can be positive or negative, whereas mass is only positive. As a result, gravity is always an attractive force, whereas electric forces can be attractive or repulsive.
The Meaning of "Electric Field"
Like the gravitational field of an object with mass, you should picture the electric field of a charge-bearing object (the source charge) as a continuous, immaterial substance that surrounds the source charge, filling all of space—in principle, to \(\pm \infty\) in all directions. The field exists at every physical point in space. To put it another way, the electric charge on an object alters the space around the charged object in such a way that all other electrically charged objects in space experience an electric force as a result of being in that field. The electric field, then, is the mechanism by which the electric properties of the source charge are transmitted to and through the rest of the universe. (Again, the range of the electric force is infinite.) We will see in subsequent chapters that the speed at which electrical phenomena travel is the same as the speed of light. There is a deep connection between the electric field and light.
In the next section, we describe how to determine the electric field and forces due to multiple individual source charges.
References
- National Weather Service [Internet]. Graphical forecasts . 2024. National Weather Service. (Select "Temperature" and set the units to Celsius.) (Public domain)
- National Weather Service [Internet]. Graphical forecasts . 2024. National Weather Service. (Select "Wind Speed".) (Public domain)
- Wikipedia contributors. Euclidean distance [Internet]. Wikipedia, The Free Encyclopedia.
- Wikimedia Commons contributors. File: Graph-paper.svg [Internet]. Wikimedia Commons. (CC-SA 3.0, Bobarino). Additional elements by Ronald Kumon (CC-BY-SA 4.0, Ronald Kumon).


1.E: The Study of Life (Exercises)
1.1: The Nature of Science
Multiple Choice
Which of the following sciences is not considered a natural science?
A. biology
B. astronomy
C. physics
D. computer science
- Answer
-
D
The type of logical thinking that uses related observations to arrive at a general conclusion is called ________.
A. deductive reasoning
B. inductive reasoning
C. hypothesis-based science
D. the scientific method
- Answer
-
B
The process of ________ helps to ensure that a scientist’s research is original, significant, logical, and thorough.
A. publication
B. public speaking
C. peer review
D. the scientific method
- Answer
-
C
A person notices that her houseplants that are regularly exposed to music seem to grow more quickly than those in rooms with no music. As a result, she determines that plants grow better when exposed to music. This example most closely resembles which type of reasoning?
A. inductive reasoning
B. deductive reasoning
C. neither, because no hypothesis was made
D. both inductive and deductive reasoning
- Answer
-
A
Free Response
Name two topics that are likely to be studied by biologists, and two areas of scientific study that would fall outside the realm of biology.
- Answer
-
Answers will vary.
Example: Two topics studied by biologists might include the genetic basis for an inherited disease and the mating behaviors of the North American Grizzly Bear. Two areas of scientific study that fall outside the realm of biology include astronomy and geology.
Thinking about the topic of cancer, write a basic science question and an applied science question that a researcher interested in this topic might ask.
- Answer
-
Answers will vary.
Example: A basic science question related to cancer might be, " How does gene expression of a particular gene change in cancerous cells compared to healthy cells?" An applied science question could be, " How well does a particular drug molecule target cancer cells and what effect does this targeting have on drug side effects experienced by the patient?"
1.2: The Scientific Process
Multiple Choice
A suggested and testable explanation for an event is called a ________.
A. hypothesis
B. variable
C. theory
D. control
- Answer
-
A
The thing (or things) that you are measuring as the outcome of your experiments are called ________.
A. independent variables
B. controlled variables
C. confounding variables
D. dependent variables
- Answer
-
D
Free Response
Although the scientific method is used by most of the sciences, it can also be applied to everyday situations. Think about a problem that you may have at home, at school, or with your car, and apply the scientific method to solve it.
- Answer
-
Answers will vary. One example of how the scientific method can be applied to an everyday situation is as follows:
- Observation: My television won't turn on
- Question: Why will my television not turn on?
- Hypothesis: The batteries in the remote are no longer working.
- Prediction: If the batteries (independent variable) are replaced then the remote will work and the TV will turn on (dependent variable).
- Experiment: Replace the batteries and attempt to turn on the the TV.
- Analyze: The TV did turn on!
- Conclusion: My hypothesis was correct. The batteries were no longer functional and replacing them solved the problem.
1.3: Themes and Concepts of Biology
Multiple Choice
Viruses are not considered living because they ________.
A. lack nuclei
B. are not made of cells
C. do not contain DNA or RNA
D. cannot reproduce
- Answer
-
B
The smallest unit of biological structure that meets the functional requirements of “living” is the ________.
A. organ
B. organelle
C. cell
D. macromolecule
- Answer
-
C
Which of the following sequences represents the hierarchy of biological organization from the most complex to the least complex level?
A. organelle, tissue, biosphere, ecosystem, population
B. organ, organism, tissue, organelle, molecule
C. organism, community, biosphere, molecule, tissue, organ
D. biosphere, ecosystem, community, population, organism
- Answer
-
D
Free Response
Select two items that biologists agree are necessary in order to consider an organism “alive.” For each, give an example of a nonliving object that otherwise fits the definition of “alive.”
- Answer
-
Answers will vary.
Example: Living things must be able to reproduce their own kind. An robot might exhibit many of the other properties of life (order, response to stimuli) but it can not reproduce.
Consider the levels of organization of the biological world, and place each of these items in order from smallest level of organization to most encompassing: skin cell, elephant, water molecule, planet Earth, tropical rainforest, hydrogen atom, wolf pack, liver.
- Answer
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Hydrogen atom, water molecule, skin cell, liver, elephant, wolf pack, tropical rainforest, planet Earth
Using examples, explain how biology can be studied from a microscopic approach to a global approach.
- Answer
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Researchers can approach biology from the smallest to the largest, and everything in between. For instance, an ecologist may study a population of individuals, the population’s community, the community’s ecosystem, and the ecosystem’s part in the biosphere. When studying an individual organism, a biologist could examine the cell and its organelles, the tissues that the cells make up, the organs and their respective organ systems, and the sum total—the organism itself.
Contributors and Attributions
Remixed and/or curated from the following works:
Clark, M. A., Douglas, M., & Choi, J. (2018). 1.1.7 Review Questions and 1.1.8 Critical Thinking Questions . In Biology 2e . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/biology-2e/pages/1-introduction ).


22.4: Oropharyngeal and Nasopharyngeal Suctioning Checklist and Sample Documentation
Suctioning via the oropharyngeal (mouth) and nasopharyngeal (nasal) routes is performed to remove accumulated saliva, pulmonary secretions, blood, vomitus, and other foreign material from these areas that cannot be removed by the patient’s spontaneous cough or other less invasive procedures. Nasal and pharyngeal suctioning are performed in a wide variety of settings, including critical care units, emergency departments, inpatient acute care, skilled nursing facility care, home care, and outpatient/ambulatory care. Suctioning is indicated when the patient is unable to clear secretions and/or when there is audible or visible evidence of secretions in the large/central airways that persist in spite of the patient’s best cough effort. Need for suctioning is evidenced by one or more of the following:
- Visible secretions in the airway
- Chest auscultation of coarse, gurgling breath sounds, rhonchi, or diminished breath sounds
- Reported feeling of secretions in the chest
- Suspected aspiration of gastric or upper airway secretions
- Clinically apparent increased work of breathing
- Restlessness
- Unrelieved coughing [1]
In emergent situations, a provider order is not necessary for suctioning to maintain a patient’s airway. However, routine suctioning does require a provider order.
For oropharyngeal suctioning, a device called a Yankauer suction tip is typically used for suctioning mouth secretions. A Yankauer device is rigid and has several holes for suctioning secretions that are commonly thick and difficult for the patient to clear. See Figure \(\PageIndex{1}\) [2] for an image of a Yankauer device. In many agencies, Yankauer suctioning can be delegated to trained assistive personnel if the patient is stable, but the nurse is responsible for assessing and documenting the patient’s respiratory status.
Yankauer suction devices are made of rigid firm plastic. The nurse or assistive personnel who performs suctioning with these devices should use care to protect the patient’s soft mucous membranes and prevent unnecessary trauma.
Nasopharyngeal suctioning removes secretions from the nasal cavity, pharynx, and throat by inserting a flexible, soft suction catheter through the nares. This type of suctioning is performed when oral suctioning with a Yankauer is ineffective. See Figure \(\PageIndex{2}\) [3] for an image of a sterile suction catheter.
Extension tubing is used to attach the Yankauer or suction catheter device to a suction canister that is attached to wall suction or a portable suction source. The amount of suction is set to an appropriate pressure according to the patient’s age. See Figure \(\PageIndex{3}\) [4] for an image of extension tubing attached to a suction canister that is connected to a wall suctioning source.
Follow agency policy regarding setting suction pressure. Pressure should not exceed 150 mm Hg because higher pressures have been shown to cause trauma, hypoxemia, and atelectasis. The following ranges are appropriate pressure according to the patient’s age:
- Neonates: 60-80 mm Hg
- Infants: 80-100 mm Hg
- Children: 100-120 mm Hg
- Adults: 100-150 mm Hg
Suction only when clinically indicated and for up to 15 seconds at a time to decrease the risk of respiratory complications. Hyperoxygenation and hyperventilation should be performed prior to the nasal and tracheal procedures to avoid the most common hazards of suctioning (hypoxemia, arrhythmias, and atelectasis). For nasal suctioning, increase the amount of O2 the patient is receiving for a few minutes prior to the procedure and instruct the patient to take several deep breaths. For tracheal suctioning, do the same. If the patient is on a ventilator, you can either hyperoxygenate and ventilate with the Ambu bag or provide a few extra machine assisted breaths prior to the procedure. Allow the patient to recover and hyperventilate and hyperoxygenate between each passing of the suction catheter. The patient should recover for 30-60 seconds between passes. [5]
When performing nasal suctioning, have the patient lean their head backwards to open the airway. This helps guide the catheter toward the trachea rather than the esophagus.
Checklist for Oropharyngeal or Nasopharyngeal Suctioning
Use the checklist below to review the steps for completion of “Oropharyngeal or Nasopharyngeal Suctioning.”
Steps
Disclaimer: Always review and follow agency policy regarding this specific skill.
- Gather supplies: Yankauer or suction catheter, suction machine or wall suction device, suction canister, connecting tubing, pulse oximeter, stethoscope, PPE (e.g., mask, goggles or face shield, nonsterile gloves), sterile gloves for suctioning with sterile suction catheter, towel or disposable paper drape, nonsterile basin or disposable cup, and normal saline or tap water.
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Perform safety steps:
- Perform hand hygiene.
- Check the room for transmission-based precautions.
- Introduce yourself, your role, the purpose of your visit, and an estimate of the time it will take.
- Confirm patient ID using two patient identifiers (e.g., name and date of birth).
- Explain the process to the patient.
- Be organized and systematic.
- Use appropriate listening and questioning skills.
- Listen and attend to patient cues.
- Ensure the patient’s privacy and dignity.
- Assess ABCs.
- Adjust the bed to a comfortable working height and lower the side rail closest to you.
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Position the patient:
- If conscious, place the patient in a semi-Fowler’s position.
- If unconscious, place the patient in the lateral position, facing you.
- Move the bedside table close to your work area and raise it to waist height.
- Place a towel or waterproof pad across the patient’s chest.
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Adjust the suction to the appropriate pressure:
- Adults and adolescents: no more than 150 mm Hg
- Children: no more than 120 mmHg
- Infants: no more than 100 mm Hg
- Neonates: no more than 80 mm Hg
For a portable unit:
- Adults: 10 to 15 cm Hg
- Adolescents: 8 to 15 cm Hg
- Children: 8 to 10 cm Hg
- Infants: 8 to 10 cm Hg
- Neonates: 6 to 8 cm Hg
- Put on a clean glove and occlude the end of the connection tubing to check suction pressure.
- Place the connecting tubing in a convenient location (e.g., at the head of the bed).
- Open the sterile suction package using aseptic technique. (NOTE: The open wrapper or container becomes a sterile field to hold other supplies.) Carefully remove the sterile container, touching only the outside surface. Set it up on the work surface and fill with sterile saline using sterile technique.
- Place a small amount of water-soluble lubricant on the sterile field, taking care to avoid touching the sterile field with the lubricant package.
- Increase the patient’s supplemental oxygen level or apply supplemental oxygen per facility policy or primary care provider order.
- Don additional PPE. Put on a face shield or goggles and mask.
- Don sterile gloves. The dominant hand will manipulate the catheter and must remain sterile.
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The nondominant hand is considered clean rather than sterile and will control the suction valve on the catheter.
- In the home setting and other community-based settings, maintenance of sterility is not necessary.
- With the dominant gloved hand, pick up the sterile suction catheter. Pick up the connecting tubing with the nondominant hand and connect the tubing and suction catheter.
- Moisten the catheter by dipping it into the container of sterile saline. Occlude the suction valve on the catheter to check for suction.
- Encourage the patient to take several deep breaths.
- Apply lubricant to the first 2 to 3 inches of the catheter, using the lubricant that was placed on the sterile field.
- Remove the oxygen delivery device, if appropriate. Do not apply suction as the catheter is inserted. Hold the catheter between your thumb and forefinger.
- Insert the catheter. For nasopharyngeal suctioning, gently insert the catheter through the naris and along the floor of the nostril toward the trachea. Roll the catheter between your fingers to help advance it. Advance the catheter approximately 5 to 6 inches to reach the pharynx. For oropharyngeal suctioning, insert the catheter through the mouth, along the side of the mouth toward the trachea. Advance the catheter 3 to 4 inches to reach the pharynx.
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Apply suction by intermittently occluding the suction valve on the catheter with the thumb of your nondominant hand and continuously rotate the catheter as it is being withdrawn.
[6]
- Suction only on withdrawal and do not suction for more than 10 to 15 seconds at a time to minimize tissue trauma.
- Replace the oxygen delivery device using your nondominant hand, if appropriate, and have the patient take several deep breaths.
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Flush the catheter with saline. Assess the effectiveness of suctioning by listening to lung sounds and repeat, as needed, and according to the patient’s tolerance. Wrap the suction catheter around your dominant hand between attempts:
- Repeat the procedure up to three times until gurgling or bubbling sounds stop and respirations are quiet. Allow 30 seconds to 1 minute between passes to allow reoxygenation and reventilation. [7]
- When suctioning is completed, remove gloves from the dominant hand over the coiled catheter, pulling them off inside out.
- Remove the glove from the nondominant hand and dispose of gloves, catheter, and the container with solution in the appropriate receptacle.
- Assist the patient to a comfortable position. Raise the bed rail and place the bed in the lowest position.
- Turn off the suction. Remove the supplemental oxygen placed for suctioning, if appropriate.
- Remove face shield or goggles and mask; perform hand hygiene.
- Perform oral hygiene on the patient after suctioning.
- Reassess the patient’s respiratory status, including respiratory rate, effort, oxygen saturation, and lung sounds.
- Assist the patient to a comfortable position, ask if they have any questions, and thank them for their time.
-
Ensure safety measures when leaving the room:
- CALL LIGHT: Within reach
- BED: Low and locked (in lowest position and brakes on)
- SIDE RAILS: Secured
- TABLE: Within reach
- ROOM: Risk-free for falls (scan room and clear any obstacles)
- Perform hand hygiene.
- Document the procedure and related assessment findings. Report any concerns according to agency policy.
Sample Documentation
Sample Documentation of Expected Findings
Patient complaining of not being able to cough up secretions. Order was obtained to suction via the nasopharyngeal route. Procedure explained to the patient. Vital signs obtained prior to procedure were heart rate 88 in regular rhythm, respiratory rate 28/minute, and O2 sat 88% on room air. Coarse rhonchi present over anterior upper airway. No cyanosis present. Patient tolerated procedure without difficulties. A small amount of clear, white, thick sputum was obtained. Post-procedure vital signs were heart rate 78 in regular rhythm, respiratory rate 18/minute, and O2 sat 94% on room air. Lung sounds clear and no cyanosis present.
Sample Documentation of Unexpected Findings
Patient complaining of not being able to cough up secretions. Order was obtained to suction via the nasopharyngeal route. Procedure explained to the patient. Vital signs obtained prior to procedure were heart rate 88 in regular rhythm, respiratory rate 28/minute, and O2 sat 88% on room air. Coarse rhonchi present over anterior upper airway. No cyanosis present. After first pass of suctioning, patient began coughing uncontrollably. Procedure was stopped and emergency assistance was requested from the respiratory therapist. Post-procedure vital signs were heart rate 78 in regular rhythm, respiratory rate 18/minute, and O2 sat 94% on room air. Coarse rhonchi continued to be present over anterior upper airway but no cyanosis present. Dr. Smith notified and a STAT order was received for a chest X-ray and to call with results.
- American Association for Respiratory Care. (2004). AARC clinical practice guideline: Nasotracheal suctioning - 2004 revision & update. Respiratory Care, 49 (9), 1080-1084. https://www.aarc.org/wp-content/uploads/2014/08/09.04.1080.pdf ↵
- “ Yankauer Suction Tip.jpg ” by Thomasrive is licensed under CC BY-SA 3.0 ↵
- “DSC_0210-150x150.jpg” by British Columbia Institute of Technology is licensed under CC BY 4.0. Access for free at https://opentextbc.ca/clinicalskills/chapter/5-7-oral-suctioning/ ↵
- “DSC_0206-e1437445438554.jpg” by British Columbia Institute of Technology is licensed under CC BY 4.0. Access for free at https://opentextbc.ca/clinicalskills/chapter/5-7-oral-suctioning/ ↵
- American Association for Respiratory Care. (2010). AARC clinical practice guideline: Endotracheal suctioning of mechanically ventilated patients with artificial airways 2010. Respiratory Care, 55 (6), 758-764. www.rcjournal.com/cpgs/pdf/06.10.0758.pdf↵
- Oronasopharyngeal suctioning. (2020). Lippincott procedures. http://procedures.lww.com ↵
- Oronasopharyngeal suctioning. (2020). Lippincott procedures. http://procedures.lww.com ↵


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3.E: Composition of Substances and Solutions- Homework
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For Chapter 3 you MUST know:
-
The additional polyatomic ions: cyanide ( \(\ce{CN^-}\)), nitrite ( \(\ce{NO_2^-}\)), and sulfite ( \(\ce{SO_3^{2-}}\)).
Turn in your answers for the following questions - show your work
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For the following molecules; write the chemical formula, determine the molecular weight and determine the number of moles in exactly 1 gram.
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carbon dioxide
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iron (II) chloride
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dinitrogen pentoxide
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iron (III) sulfate
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Name the following compounds, determine the molecular weight and determine how many moles in 8.35 grams of the compound.
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KI
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CaF
2
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Cu
2
SO
4
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N
2
O
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LiOH
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Give the chemical formula (or atomic symbol), molecular (or atomic) weight, and charge for the following ions:
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sulfate
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sulfite
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nitrate
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chloride
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nitride
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acetate
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carbonate
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Calculate the number of moles in:
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45.3594 g of Ne
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0.198669 g of Ne
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Calculate the mass of:
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2.00 mole of Fe
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4.362 x 10
-5
mol of Fe
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Describe how to prepare 250 mL of 0.12 M lithium chloride solution from solid lithium chloride.
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Describe how to prepare 100 mL of 0.012 M lithium chloride solution from a 0.12 M lithium chloride solution.
The Following Questions are for your practice - Do Not Turn In. They include answers so you can check your work
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What is the total mass (amu) of carbon in each of the following molecules?
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CH
4
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C
12
H
10
O
6
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(a)
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12.01 amu
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(b)
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144.12 amu
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Calculate the molecular or formula mass of each of the following:
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P
4
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H
2
O
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Ca(NO
3
)
2
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(a)
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123.896 amu
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(b)
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18.015 amu
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(c)
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164.086 amu
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Determine the molecular mass of the following compounds:
-
-
-
(a)
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56.107 amu
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(b)
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54.091 amu
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Calculate the molar mass of each of the following:
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S
8
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C
5
H
12
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(a)
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256.528 g/mol
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(b)
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72.150 g mol
−1
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Determine the mass of each of the following:
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0.0146 mol KOH
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10.2 mol ethane, C
2
H
6
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(a)
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0.819 g
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(b)
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307 g
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answer
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Mg
3
Si
2
H
3
O
8
(empirical formula), Mg
6
Si
4
H
6
O
16
(molecular formula)
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Calculate the percent composition of ammonia, NH
3
to four significant figures:
-
answer
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% N = 82.24%; % H = 17.76%
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A compound of carbon and hydrogen contains 92.3% C and has a molar mass of 78.1 g/mol. What is its molecular formula?
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answer
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C
6
H
6
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Determine the empirical and molecular formula for chrysotile asbestos. Chrysotile has the following percent composition: 28.03% Mg, 21.60% Si, 1.16% H, and 49.21% O. The molar mass for chrysotile is 520.8 g/mol.
3.3: Molarity
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Determine the molarity for 0.444 mol of CoCl
2
in 0.654 L of solution
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answer
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0.679
M
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Determine the molarity for 98.0 g of phosphoric acid, H
3
PO
4
, in 1.00 L of solution
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answer
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1.00
M
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Calculate the number of moles and the mass of the solute in 2.00 L of 18.5
M
H
2
SO
4
, concentrated sulfuric acid:
-
answer
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37.0 mol H
2
SO
4
; 3.63 × 10
3
g H
2
SO
4
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Calculate the molarity of 0.195 g of cholesterol, C
27
H
46
O, in 0.100 L of serum, the average concentration of cholesterol in human serum
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answer
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5.04 × 10
−3
M
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What is the molarity of the diluted solution when 1.00 L of a 0.250-
M
solution of Fe(NO
3
)
3
is diluted to a final volume of 2.00 L?
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answer
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0.125
M
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What volume of a 0.20-
M
K
2
SO
4
solution contains 57 g of K
2
SO
4
?
-
answer
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1.6 L


11.8: Lab 1- Chi-Square Goodness-of-Fit (Worksheet)
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Name: ______________________________
Section: _____________________________
Student ID#:__________________________
Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.
Student Learning Outcome
- The student will evaluate data collected to determine if they fit either the uniform or exponential distributions.
Collect the Data
Go to your local supermarket. Ask 30 people as they leave for the total amount on their grocery receipts. (Or, ask three cashiers for the last ten amounts. Be sure to include the express lane, if it is open.)
You may need to combine two categories so that each cell has an expected value of at least five.
 Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
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Calculate the following:
- \(\bar{x} =\)________
- \(s =\) ________
- \(s^{2} =\) ________
Uniform Distribution
Test to see if grocery receipts follow the uniform distribution.
- Using your lowest and highest values, \(X \sim U (\)_______, _______\()\)
- Divide the distribution into fifths.
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Calculate the following:
- lowest value = _________
- 20 th percentile = _________
- 40 th percentile = _________
- 60 th percentile = _________
- 80 th percentile = _________
- highest value = _________
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For each fifth, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
Fifth Observed Expected 1 st 2 nd 3 rd 4 th 5 th - \(H_{0}\): ________
- \(H_{a}\): ________
- What distribution should you use for a hypothesis test?
- Why did you choose this distribution?
- Calculate the test statistic.
- Find the \(p\text{-value}\).
- Sketch a graph of the situation. Label and scale the x -axis. Shade the area corresponding to the \(p\text{-value}\).
- State your decision.
- State your conclusion in a complete sentence.
Exponential Distribution
Test to see if grocery receipts follow the exponential distribution with decay parameter \(\frac{1}{\bar{x}}\).
- Using \(\frac{1}{\bar{x}}\) as the decay parameter, \(X \sim \text{Exp}(\)_________\()\).
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Calculate the following:
- lowest value = ________
- first quartile = ________
- 37 th percentile = ________
- median = ________
- 63 rd percentile = ________
- 3 rd quartile = ________
- highest value = ________
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For each cell, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
Cell Observed Expected 1 st 2 nd 3 rd 4 th 5 th 6 th - \(H_{0}\): ________
- \(H_{a}\): ________
- What distribution should you use for a hypothesis test?
- Why did you choose this distribution?
- Calculate the test statistic.
- Find the \(p\text{-value}\).
- Sketch a graph of the situation. Label and scale the x -axis. Shade the area corresponding to the \(p\text{-value}\).
- State your decision.
- State your conclusion in a complete sentence.
Discussion Questions
- Did your data fit either distribution? If so, which?
- In general, do you think it’s likely that data could fit more than one distribution? In complete sentences, explain why or why not.


7.10: Words of Wisdom- It’s Like Online Dating
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Jackie Vetrano
Jackie Vetrano
Searching for a job, especially your first job, is a lot like online dating. It begins as a time commitment, gets nerve-wracking towards the middle, but ends in success and happiness if you follow the right process.
Like many single people with access to current technology, I ventured into the world of online dating. I went for coffee with potential mates who were instant no way s, some who left me scratching my head, and a few who I found a connection with.
But hang on. We are here to talk about professional development, not my love life.
Being on the job hunt is not easy. Many spend hours preparing résumés, looking at open positions, and thinking about what career path to travel. Occasionally, it is overwhelming and intimidating, but when taken one step at a time, it can be a manageable and an exciting process.
Your Dating Profile—The Résumé
The first step of online dating is the most important: create your dating profile. Your profile is where you put your best foot forward and show off all of your attractive qualities through visuals and text. Online daters find their most flattering photos and then season the “about me” section of their profile with captivating and descriptive words to better display who they are and why other online daters should give them a shot.
Résumés follow this same logic. Your résumé should be clean, polished, and present you in your best light for future employers. Like dating profiles, they are detailed and should paint a picture for other prospective dates (or future employers) supporting why you deserve a chance at their love—an interview.
The unspoken rules of online dating profiles are very similar to the rules for writing a résumé. Whether you like it or not, your online dating profile and résumé both serve as a first impression. Profiles and résumés that are short, filled with spelling errors, or vague are usually passed over. Your written description is very important to display who you are.
 Knowing your audience is a key factor in crafting the perfect résumé. Logically, if my online dating profile presented studious and quiet personality traits, I would likely start receiving messages from potential mates who are looking for someone who is seeking those traits. By taking a similar approach while writing a résumé, you can easily determine the tone, language, and highlighted skills and experiences you should feature. The tone of your résumé is dictated by the nature of the position you hope to obtain in the future. For example, hospitality jobs or positions that require you to interact with many people on a daily basis should be warm and welcoming while analytical jobs, such as accounting or research positions, should reflect an astute attention to detail. Your choice in language follows similar logic—use appropriate terms for the position you are seeking.
Unlike online dating profiles, your résumé should include your important contact information, including email address and telephone number.
Finding Love—The Job Hunt
Simply crafting an online dating profile doesn’t necessarily mean you will find your one true love, and the same applies to your career. Once your résumé is crafted, it is equally as important to search the job market to find what you think would be a good fit based on your skills and preferences.
An important part of online dating is setting the appropriate search filters. Sites allow users to search by gender, location, age, religious beliefs, or social practices. All these are small pieces that affect the overall compatibility between two people, with some factors being more important than others. By carefully choosing which filters are most important, you’re sure to have better luck finding a perfect match that will make you happy and excited.
As you begin the job hunt, it is important to determine your filters when it comes to a career or first job. Some of these filters, like dating, may hold more weight to you than others. Many job search sites allow users to find job listings as defined by these filters, and they can include: location, type of organization, starting salary, potential for promotion, job responsibilities, etc.
Always establish filters. You may say, “I don’t care what I find, as long as I find something .” All of us have a preference in our love lives as well as our careers, and being honest with yourself about these filters will increase the likelihood for happiness in the end. These filters also allow you to more quickly read through job postings, because you will be focusing on positions with the qualities that you already determined are the most important to you.
When you are searching for a posted position using an online service, enter your filters and try a variety of search phrases to find as many postings as possible. Even changing “school counselor” to “guidance counselor” or only “counseling” may produce a different set of job postings, depending on the website.
It is also important to remember, like online dating sites, not every job posting will be on every employment site. Experiment with different search techniques and websites, and seek the advice of others for the best resource for recent postings. It’s easy to save these filters and search results on most job search websites, allowing you to check back on a constant basis without resetting your filters. Most sites also allow you to create a free account, providing you a way to receive email alerts any time a new job is posted and fits in with your filters.
After the filters are set, it is time to start the exciting and nerve-wracking part: scrolling through profiles.
Scrolling through Profiles—The Job Postings
You will find attractive potentials with no description provided, others who exclusively take selfies, and a whole list of people who simply are not right for you based on their description. But then, it happens. You find someone who may be a match, and your heart starts to flutter.
Reading through a job description is equally as exciting. A good job posting provides a robust description of responsibilities, minimum qualifications, and desired qualifications for candidates. Knowing your own skill set, you can determine if you’re a match or not. By having honest filters set before searching, it’s likely that you are.
Sometimes, online dating simply doesn’t work. Many will then turn to speed dating to meet new people in the area. This method allows for daters to quickly determine whether or not there’s any chemistry, without spending time searching through online profiles. Similarly, job fairs provide this quick face-to-face advantage. If you’re attending a job fair, be sure dress appropriately and have copies of your résumé and business cards on hand. Through job fairs, you’ll be building your first impression right away, and may even be offered an interview on the spot.
Sending a Message—The Cover Letter
After searching through dozens of profiles, online daters generally find a handful of people they can picture themselves with. There’s only one way to find out more about the person, and that’s by sending the first message.
My personal rule for online dating is to always send a thoughtful first message to those I want to meet. It’s easy enough to send a short, impersonal “hey,” but it’s important to make a good impression. It’s obvious that the message I send, combined with my well-written profile, is going to continue to form a first impression of me. First impressions are very important in dating, job-hunting, and life overall.
The challenging part of the first message I send through online dating sites is determining what to say. I’ve never met these people before, but I do have access to their dating profiles filled with their hobbies, hometowns, and more. This is a perfect starting point for my message, especially if we both root for the same football team or if the other person likes to run as much as I do.
Your cover letter serves as an introduction to your future employer and should compliment your résumé to create a shining first impression. It is incredibly challenging to sit in front of a blank screen trying to find a good starting point, which means you should look at the job posting and organization’s website for ideas about what to include.
Generally, these job postings provide a set of hard skills (such as proficiency with certain technology) and soft skills (such as public speaking, teamwork, or working in a flexible environment) required and desired for the posted position. This information provides you a list of what should be explained in your cover letter. Demonstrating your hard skills is a simple enough task by using examples or stating certifications, but describing your soft skills may require a little more thought. These soft skills can be exhibited by discussing specific examples of past experiences in previous jobs you’ve held, volunteer work, or work you’ve done in college classes.
After you have crafted your cover letter, you should send it to a few people you trust for their opinion and overall proofreading along with the job posting for their reference. It’s obvious that your cover letter should be free of spelling and grammar errors, but these trustworthy individuals will also be able to provide helpful insight about the examples you’ve used to display your soft skills.
The Hard Part—Waiting
You just sent your first message to the love of your life, but now what? You wait. You will undoubtedly feel anxious, especially if you sit refreshing your inbox for hours at a time, but if you made a good first impression and they like you as much as you like them, you will hear back.
While you wait, take the time to do a little research. Search for the organization online and view what information they provide. You will be storing up some good facts about your future partner, which is something you can bring up when you’re on your first date. This research will also allow you to understand the company better. The organization displays their values, work ethic, and personality through online and print resources, which allows you to see if their values match with yours.
Unlike online dating, it is helpful to follow up with an organization you’ve applied to. Generally, the Human Resources department of an organization is the best place to start if you are unsure whom to call. This phone call is another piece of your first impression, which means you should be prepared to talk. Have any materials that you need ready, and be sure you are in a quiet place.
The First Date—The Job Interview
After what may feel like forever, you hear back from the love of your life. Congratulations! In the online dating world, you may chat about common interests (because you wrote a stunning first message), but in the world of work, you’ll be asked to visit the organization for an interview.
I have been on many first dates, and whether it’s in a coffee shop or over dinner, the first face-to-face meeting is tremendously important. If someone I am meeting for the first time looks like they just came from the gym or rolled out of bed, my impression instantly changes. This same theory can be directly applied to your first date with your future employer. You have worked hard on your cover letter and résumé, and you should not taint the sparkling first impression you have created with the wrong choice in dress.
What you wear to a job interview may change based on the position you have applied for, but there are a set of basic rules that everyone should follow. Similar to meeting someone on a first date for coffee, you want to be comfortable. Some interviews may take place with multiple people in an organization, meaning you will be walking to different locations, sitting down, and potentially sweating from a broken air conditioning unit. Consider these factors when choosing your outfit for your interview, and if you’re concerned about being underdressed, remember to always dress a bit nicer than how you’d dress for the job itself.
There is nothing worse than sitting alone at a coffee shop waiting for a mystery date to show up. It’s uncomfortable and affects my overall first impression of whom I’m about to meet. Avoid making your mystery employer annoyed and waiting for you by leaving at least ten minutes earlier than you need to, just in case you get stuck in traffic. Arrive at least ten minutes early. The interview will start out much better if you are early rather than nervous and running late. Arriving early also gives you the time to have some coffee and review materials you may need for the interview. Coming on time to an interview or a first date shows you respect the time of the person you plan to meet.
On a first date, it is all about communication. Sometimes, there may be silences that cannot be filled or the person I have just met discloses their entire life story to me in less than an hour. If we cannot achieve a proper balance, there will not be a second date. Communicating effectively in a job interview is equally as important, especially if you want a job offer!
All of the rules of dating apply to how you should behave in a job interview. The interviewer will ask you questions, which means that you should look at them and focus on what is being asked. Your phone should be on silent (not even on vibrate), and hidden, to show that you are fully attentive and engaged in the conversation you are having. Much like having a conversation on a date, the answers to your questions should be clear and concise and stay on topic. The stories I tell on my first dates are more personal than what would be disclosed in a job interview, but the mindset is the same. You are building the impression that the organization has of you, so put your best foot forward through the comments you make.
To make that great impression, it is really important to heavily prepare and practice, even before you have an interview scheduled. By brainstorming answers to typical interview questions in a typed document or out loud, later during the interview you will easily remember the examples of your past experiences that demonstrate why you are best for the job. You can continue to update this list as you move through different jobs, finding better examples to each question to accurately describe your hard and soft skills.
This interview is as much a date for your future employer as it is for you. Come prepared with questions that you have about the company, the position, and anything else you are curious about. This is an opportunity for you to show off the research you’ve done on the organization and establish a better understanding of company culture, values, and work ethic. Without knowing these basics of the company or organization, what you thought was a match might only end in a tense breakup.
After your interview is over, you continue to have an opportunity to build on the positive impression that you’ve worked hard to form. Sending a follow up thank you note to each person you interviewed with will show your respect for the time the organization spent with you. These notes can be written and sent by mail or emailed, but either way should have a personal touch, commenting on a topic that was discussed in the interview. While sending a thank you note after a first date may sound a little strange, you might not get asked to a second interview without one!
It’s Official—The Job Offer
In the online dating world, it takes a few dates to determine if two people are a match. In the corporate world, you may have a one or two interviews to build a relationship. If your impression was positive and the organization believes you’re a match for the open position, you’ll be offered a job.
With a job offer also comes the salary for the position. It is important to know what a reasonable salary is for the position and location, which can be answered with a bit of research. One good place to look is the Bureau of Labor Statistics website: http://stats.bls.gov/oes/current/oessrcst.htm . At this point, it is not uncommon to discuss your salary with your future employer, but be sure to do so in a polite way.
Online dating sites provide the means for millions of people to meet future partners, and the number of people who use online dating is so large that there are sure to be disappointments along the way. I have met people who I thought were compatible with me, but they did not feel the same, and vice versa. This happens frequently while searching for a job, which can be discouraging, but should not hinder you from continuing to search! There are a great number of opportunities, and sometimes all it takes is adjusting your filters or revising your résumé and cover letter. The cliché “there’s plenty of fish in the sea” may be true, but there is definitely a way for each person to start their career off right.
Licenses and Attributions:
CC licensed content, Shared previously:
Foundations of Academic Success: Words of Wisdom. Edited by Thomas Priester. Essay authored by Jackie Vetrano. Located at: https://milnepublishing.geneseo.edu/foundations-of-academic-success/chapter/its-like-online-dating/ License: CC BY: Attribution.
Adaptions: Some content edited by Dave Dillon based on peer review suggestions.


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Evaluating and understanding the function of case law is vital to the learning the criminal court process. Using the website Oyez or Justia US Law, research an influential criminal court case law. Select a case from the list below and provide the following information: facts of the case (case name, parties, what happened, and judgement), issues (what is in dispute), holding (the applied rule of law), and rationale (reason for the holding). Choose from the following cases:
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Knowles v. Iowa (1998)
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Indianapolis v. James (2001)
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Kyllo v. United States (2001)
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Ferguson v. City of Charleston (2001)
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Groh v. Ramirez (2004)
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Hudson v. Michigan (2006)
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After examining case law, explain how case law provides clarification, expectations, or interpretation of the Constitution. Why is the Supreme Court so important to the criminal court process? Select one of the Constitutional Amendments discussed in the chapter, and using the internet, conduct a search of case law that addresses the amendment. For example: 5th Amendment Search – Case law and the 5th Amendment
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“Society uses laws (rules designed to control citizens’ behaviors) so that these behaviors will conform to societal norms, cultures, mores, traditions, and expectations.” As our society continues to become more heterogeneous and more norms/cultures are present, how does the criminal process keep pace with the changes in society? How do we protect the historical intentions of the Constitution considering the changing nature of society? What are the restrictions and potential conflicts that occur?


7.2: §53. The Regular Latin Diminutive Suffixes -ULUS and -CULUS
The standard rule for Latin diminutives is quite straightforward. For nouns of the first or second declension, the regular diminutive suffix is -ulus (M), -ula (F), or -ulum (N), depending upon the gender of the original noun; for words of the third, fourth, or fifth declensions, the suffix is -culus , -cula , -culum . As the suffix will suggest, the gender of the original noun is maintained in the gender of its diminutive.
Let’s first consider the -ulus -ula -ulum type. If we take the Latin 1st declension feminine noun forma (“shape,” “form”), we discover that its diminutive is form- (word base) + -ula (suffix) = formula (“little shape,” “little form”). It was as simple as that, in Latin. From the English vantage point, it’s often slightly harder, because there aren’t many Latin diminutives that have come into English so totally unchanged as formula . Let’s try the 2nd declension masculine noun modus (“measure,” “manner”); a “little measure” is a mod-ulus , the transparent origin of the English word module . In the same fashion, Latin nodus (“knot,” “node”) produced the diminutive nod-ulus (“little knot”), and the English derivative nodule . To an ancient Roman, the word circus meant the great race-course in the city, the Circus Maximus; a “little circus” is a circ-ulus , only slightly disguised as English circle . For a 2nd declension neuter example we can choose granum , “a [kernel of] grain.” Its predictable diminutive was gran-ulum , English granule .
What about the -culus -cula -culum suffix of the 3rd, 4th, and 5th declensions? Joined to the original word with or without the connecting vowel -i- , it presents no serious problems. If you diminish pars , part-is, F (“part”), you get part-i-cula (“little part”), English particle . From the 4th declension noun artus , M (“joint’) comes the diminutive art-i-culus (“little joint”), English art icle . [1] For 3rd declension neuter nouns like corpus or opus , the suffix appears added to the nominative form, producing the diminutives corpusculum (E corpuscle ), “a little body,” and opusculum (E op ú scule ), “a small or trifling work.” The most startling etymology, no doubt, is mus-culus (E muscle ), “a little mouse.” Muscle and corpuscle are just two of perhaps a hundred or more diminutives that occur in the language of anatomy and medicine.
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In its root origins,
artus
, M (“joint”) was related to
ars
,
artis
, F (“skill,” “art”). Latin might conceivably have developed a noun
*articula
, “little art”; but there is no evidence of such a word. ↵


2.8: For Further Exploration
Articles
Ancient Astronomy
Gingerich, O. “From Aristarchus to Copernicus.” Sky & Telescope (November 1983): 410.
Gingerich, O. “Islamic Astronomy.” Scientific American (April 1986): 74.
Astronomy and Astrology
Fraknoi, A. “Your Astrology Defense Kit.” Sky & Telescope (August 1989): 146.
Copernicus and Galileo
Gingerich, O. “Galileo and the Phases of Venus.” Sky & Telescope (December 1984): 520.
Gingerich, O. “How Galileo Changed the Rules of Science.” Sky & Telescope (March 1993): 32.
Maran, S., and Marschall, L. “The Moon, the Telescope, and the Birth of the Modern World.” Sky & Telescope (February 2009): 28.
Sobel, D. “The Heretic’s Daughter: A Startling Correspondence Reveals a New Portrait of Galileo.” The New Yorker (September 13, 1999): 52.
Websites
Ancient Astronomy
Aristarchos of Samos: http://adsabs.harvard.edu//full/seri/JRASC/0075//0000029.000.html . By Dr. Alan Batten.
Claudius Ptolemy: http://www-history.mcs.st-and.ac.uk/Biographies/Ptolemy.html . An interesting biography.
Hipparchus of Rhodes: http://www-history.mcs.st-andrews.ac.uk/Biographies/Hipparchus.html . An interesting biography.
Astronomy and Astrology
Astrology and Science: http://www.astrology-and-science.com/hpage.htm . The best site for a serious examination of the issues with astrology and the research on whether it works.
Real Romance in the Stars: www.independent.co.uk/voices/the-real-romance-in-the-stars-1527970.html. 1995 newspaper commentary attacking astrology.
Copernicus and Galileo
Galileo Galilei: http://www-history.mcs.st-andrews.ac.uk/Biographies/Galileo.html . A good biography with additional links.
Galileo Project: http://galileo.rice.edu/ . Rice University’s repository of information on Galileo.
Nicolaus Copernicus: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Copernicus.html . A biography including links to photos about his life.
Videos
Astronomy and Astrology
Astrology Debunked: https://www.youtube.com/watch?v=y84HX2pMo5U . A compilation of scientists and magicians commenting skeptically on astrology (9:09).
Copernicus and Galileo
Galileo: http://www.biography.com/people/galileo-9305220 . A brief biography (2:51).
Galileo’s Battle for the Heavens: https://www.youtube.com/playlist?list=PL28AF597A9C90E18E . A NOVA episode on PBS (1:48:55)
Nicolaus Copernicus: http://www.biography.com/people/nicolaus-copernicus-9256984 . An overview of his life and work (2:41).


6.13: Probability Rules (2 of 3)
Learning Objectives
- Reason from probability distributions, using probability rules, to answer probability questions.
Here we continue to use probability distributions to answer probability questions. We look for some patterns that suggest general rules for determining probabilities.
Example
When Can We Add Probabilities?
Compare these two questions. What do the solutions have in common?
- Question 1: A person with blood type A can receive blood from individuals with type A or O blood. What is the probability that a randomly selected person from the United States can donate blood to someone with type A blood?
| Blood Type | O | A | B | AB |
| Probability | 0.45 | 0.41 | 0.10 | 0.04 |
- Answer P (donate to A) = P (blood type A or blood type O) = 0.45 + 0.41 = 0.86. There is an 86% chance that a randomly selected person in the United States can donate blood to someone with type A blood.
- Question 2: What is the probability that a randomly chosen boreal owl nest will either be empty or contain only 1 egg?
| Number of Eggs | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.2 | 0.1 | 0.1 | 0.25 | 0.25 | 0.05 | 0.05 |
- Answer P (no eggs or 1 egg) = P (no egg) + P (1 egg) = 0.2 + 0.1 = 0.3. There is a 30% chance that a randomly selected boreal owl nest will be empty or contain only one egg.
What do these solutions have in common?
In each case, we have two events and we want to find the probability that either event A or event B occurs. In each case, we added the probabilities. This works because the events have no outcomes in common. When two events have no outcomes in common, they are disjoint .
The events “type A blood” and “type O blood” are disjoint. These events cannot both happen at the same time for a single person. A person cannot have both type A blood and type O blood.
The events “no eggs” and “1 egg” are disjoint. These outcomes cannot both happen at the same time for a single nest. A nest cannot contain no eggs and at the same time contain 1 egg.
If two events are disjoint, then we can add their individual probabilities. We write this fact as a rule:
P ( A or B ) = P ( A ) + P ( B )
Comment
We stated the addition rule as a formal rule. A rule is a concise way to summarize a general principle from specific examples. This is one advantage of a rule. One disadvantage of a rule is that sometimes it discourages us from just thinking through a problem. Students often have the experience that they misremember a rule or forget the conditions required for the rule to work. This leads to mistakes that we can avoid if we just think through the problem without worrying about rules. We encourage you to think through probability problems whenever possible without resorting to rules. If you use a rule, be careful to check that the situation meets the conditions required for using the rule.
This addition rule for probabilities only works when the events are disjoint. If the events are not disjoint, the rule does not work. Here is an example of when the rule does not work because the events are not disjoint.
Example
When Can We NOT Add Probabilities?
| Arts-Sci | Bus-Econ | Info Tech | Health Science | Graphics Design | Culinary Arts | Row Totals | |
| Female | 4,660 | 435 | 494 | 421 | 105 | 83 | 6,198 |
| Male | 4,334 | 490 | 564 | 223 | 97 | 94 | 5,802 |
| Column Totals | 8,994 | 925 | 1,058 | 644 | 202 | 177 | 12,000 |
- Question: What is the probability that a randomly selected student is either a Health Science major or a female?
- Answer There are 644 Health Science majors and 6,198 females, but 421 students are counted twice because they are both Health Science majors and female. We must subtract these students before calculating the relative frequency:
- Now let’s calculate the individual probabilities and see if the rule works:
- Main point: P (Health Science or female) ≠ P (Health Science) + P (female). In other words, the addition rule does not work here. Why not? The two events “Health Science” and “female” are not disjoint. The data set contains people who are both in the Health Science program and female.
Example
Do We Ever Subtract Probabilities?
Compare these two questions. What do the solutions have in common?
- Question 1: People with blood type O can donate blood to people with any other blood type. For this reason, people with blood type O are called universal donors. What is the probability that a randomly selected person from the United States is not a universal donor?
| Blood Type | O | A | B | AB |
| Probability | 0.45 | 0.41 | 0.10 | 0.04 |
- Answer P (NOT a universal donor) = P (blood type is not type O) = P (blood type A, B, or AB) = 0.41 + 0.10 + 0.04 = 0.55. There is a 55% chance that a randomly selected person in the United States is not a universal donor.
Here is another way we can solve this problem. We can use the idea that all of the probabilities together make up 100% of the possibilities. If we add up all the probabilities in the table, we get 1. We can subtract the probability that someone is type O from 1 to find the probability that the person is not type O:
- P (NOT a universal donor) = P (blood type is not type O) = 1 – P (type O) = 1 – 0.45 = 0.55
- Question 2: What is the probability that a randomly selected boreal owl nest is not empty?
| Number of Eggs | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.2 | 0.1 | 0.1 | 0.25 | 0.25 | 0.05 | 0.05 |
- Answer P (nest is not empty) = P (at least one egg) = P (1, 2, 3, 4, 5, or 6 eggs) = 0.1 + 0.1 + 0.25 + 0.25 + 0.05 + 0.05 = 0.80. There is an 80% chance that the nest you observe has at least one egg.
Here is another approach:
- P (nest is not empty) = P (at least one egg) = 1 – P (0 eggs) = 1 – 0.2 = 0.8.
What do these solutions have in common?
In each case, we have an event that can be interpreted as a “not” statement. The probability that a person is not a universal donor means the person is not type O . The probability that a boreal owl nest is empty means the nest does not contain 0 eggs . In each case, the easy way to compute the probability is to use the complement event. The complement of event A is the event composed of outcomes that are “not A .” In our examples, the complement of “type O blood” is the event composed of “blood types A, B, or AB.” The complement of “0 eggs” is the event composed of “1, 2, 3, 4, 5, or 6 eggs.” When two sets of events are complements, their probabilities add to 1.
When one event is the complement of another, then we can use the complement rule:
P (not A ) = 1 – P ( A )
We can use this rule to find probabilities only when the two events are complements. Two events are complements when their probabilities add to 1.
Contributors and Attributions
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


9: Gravity
- Understand Kepler’s Laws.
- Understand Newton’s Universal Theory of Gravity.
- Understand Gauss’ Law and the gravitational field.
- Understand how to use energy to describe orbits.
- Understand how Einstein’s General Theory of Relativity differs from Newton’s theory of gravity.
In previous chapters, we have so far learned about Newton’s Theory of Classical Mechanics, which allowed us to model the motion of an object based on the forces acting on the object. In this chapter, we present the theories that describe the force of gravity itself. We will see several theories of gravity and focus primarily on Newton’s Universal Theory of Gravity.
A person stands on a scale at the top of Mount Logan, the tallest mountain in Canada. How will her measured weight compare to her weight at sea level?
- It will be slightly less than her weight at sea level.
- It will be equal to her weight at sea level.
- It will be slightly more than her weight at sea level.