24.E: Electromagnetic Waves (Exercises)
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Conceptual Questions
24.2: Production of Electromagnetic Waves
1. The direction of the electric field shown in each part of Figure 1 is that produced by the charge distribution in the wire. Justify the direction shown in each part, using the Coulomb force law and the definition of \(\displaystyle E = F/q\), where \(\displaystyle q\) is a positive test charge.
2. Is the direction of the magnetic field shown in Figure 2a consistent with the right-hand rule for current (RHR-2) in the direction shown in the figure?
3. Why is the direction of the current shown in each part of Figure 2 opposite to the electric field produced by the wire’s charge separation?
4. In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the wire? Explain.
Electromagnetic waves approaching long straight wires.
5. In which situation shown in the figure will the electromagnetic wave be more successful in inducing a current in the loop? Explain.
Electromagnetic waves approaching a wire loop.
6. Should the straight wire antenna of a radio be vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals? (Note that the direction of the loop that produces the best reception can be used to determine the location of the source. It is used for that purpose in tracking tagged animals in nature studies, for example.)
7. Under what conditions might wires in a DC circuit emit electromagnetic waves?
8. Give an example of interference of electromagnetic waves.
9. The figure shows the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this be used to make a directional antenna system that broadcasts preferentially in certain directions? Explain.
An overhead view of two radio broadcast antennas sending the same signal, and the interference pattern they produce.
10. Can an antenna be any length? Explain your answer.
24.3: The Electromagnetic Spectrum
11. If you live in a region that has a particular TV station, you can sometimes pick up some of its audio portion on your FM radio receiver. Explain how this is possible. Does it imply that TV audio is broadcast as FM?
12. Explain why people who have the lens of their eye removed because of cataracts are able to see low-frequency ultraviolet.
13. How do fluorescent soap residues make clothing look “brighter and whiter” in outdoor light? Would this be effective in candlelight?
14. Give an example of resonance in the reception of electromagnetic waves.
15. Illustrate that the size of details of an object that can be detected with electromagnetic waves is related to their wavelength, by comparing details observable with two different types (for example, radar and visible light or infrared and X-rays).
16. Why don’t buildings block radio waves as completely as they do visible light?
17. Make a list of some everyday objects and decide whether they are transparent or opaque to each of the types of electromagnetic waves.
18. Your friend says that more patterns and colors can be seen on the wings of birds if viewed in ultraviolet light. Would you agree with your friend? Explain your answer.
19. The rate at which information can be transmitted on an electromagnetic wave is proportional to the frequency of the wave. Is this consistent with the fact that laser telephone transmission at visible frequencies carries far more conversations per optical fiber than conventional electronic transmission in a wire? What is the implication for ELF radio communication with submarines?
20. Give an example of energy carried by an electromagnetic wave.
21. In an MRI scan, a higher magnetic field requires higher frequency radio waves to resonate with the nuclear type whose density and location is being imaged. What effect does going to a larger magnetic field have on the most efficient antenna to broadcast those radio waves? Does it favor a smaller or larger antenna?
22. Laser vision correction often uses an excimer laser that produces 193-nm electromagnetic radiation. This wavelength is extremely strongly absorbed by the cornea and ablates it in a manner that reshapes the cornea to correct vision defects. Explain how the strong absorption helps concentrate the energy in a thin layer and thus give greater accuracy in shaping the cornea. Also explain how this strong absorption limits damage to the lens and retina of the eye.
Problems & Exercises
24.1: Maxwell’s Equations: Electromagnetic Waves Predicted and Observed
23. Verify that the correct value for the speed of light c is obtained when numerical values for the permeability and permittivity of free space (\(\displaystyle mu_{0}\) and \(\displaystyle \epsilon_{0}\)) are entered into the equation \(\displaystyle c = \frac{1}{\mu_{0}\epsilon_{0}}\).
24. Show that, when SI units for \(\displaystyle \mu_{0}\) and \(\displaystyle \epsilon_{0}\) are entered, the units given by the right-hand side of the equation in the problem above are m/s.
24.2: Production of Electromagnetic Waves
25. What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of \(\displaystyle 5.00 \times 10^{-4} T\) (about 10 times the Earth’s)?
Solution
150 kV/m
26. The maximum magnetic field strength of an electromagnetic field is \(\displaystyle 5 \times 10^{-6} T\). Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is \(\displaystyle 0.75c\).
27. Verify the units obtained for magnetic field strength \(\displaystyle B\) in the in-chapter example (using the equation \(\displaystyle B = \frac{E}{c}\)) are in fact teslas (T).
24.3: The Electromagnetic Spectrum
28. (a) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each.
(b) Which frequency would produce smaller hot spots in foods due to interference effects?
Solution
(a) 33.3 cm (900 MHz) 11.7 cm (2560 MHz)
(b) The microwave oven with the smaller wavelength would produce smaller hot spots in foods, corresponding to the one with the frequency 2560 MHz.
29. (a) Calculate the range of wavelengths for AM radio given its frequency range is 540 to 1600 kHz.
(b) Do the same for the FM frequency range of 88.0 to 108 MHz.
30. A radio station utilizes frequencies between commercial AM and FM. What is the frequency of a 11.12-m-wavelength channel?
Solution
26.96 MHz
31. Find the frequency range of visible light, given that it encompasses wavelengths from 380 to 760 nm.
32. Combing your hair leads to excess electrons on the comb. How fast would you have to move the comb up and down to produce red light?
Solution
\(\displaystyle 5.0 \times 10^{14}\) Hz
33. Electromagnetic radiation having a \(\displaystyle 15.0 - \mu m\) wavelength is classified as infrared radiation. What is its frequency?
34. Approximately what is the smallest detail observable with a microscope that uses ultraviolet light of frequency \(\displaystyle 1.20 \times 10^{15} Hz\)?
Solution
\(\displaystyle \lambda = \frac{c}{f} = \frac{3.00 \times 10^{8} m/s}{1.20 \times 10^{15} Hz} = 2.50 \times 10^{-7} m\)
35. A radar used to detect the presence of aircraft receives a pulse that has reflected off an object \(\displaystyle 6 \times 10^{-5} s\) after it was transmitted. What is the distance from the radar station to the reflecting object?
36. Some radar systems detect the size and shape of objects such as aircraft and geological terrain. Approximately what is the smallest observable detail utilizing 500-MHz radar?
Solution
0.600 m
37. Determine the amount of time it takes for X-rays of frequency \(\displaystyle 3 \times 10^{18} Hz\) to travel (a) 1 mm and (b) 1 cm.
38. If you wish to detect details of the size of atoms (about \(\displaystyle 1 \times 10^{-10} m\)) with electromagnetic radiation, it must have a wavelength of about this size.
(a) What is its frequency?
(b) What type of electromagnetic radiation might this be?
Solution
(a) \(\displaystyle f = \frac{c}{\lambda} = \frac{3.00 \times 10^{8} m/s}{1 \times 10^{-10} m} = 3 \times 10^{18} Hz\)
(b) X-rays
39. If the Sun suddenly turned off, we would not know it until its light stopped coming. How long would that be, given that the Sun is \(\displaystyle 1.50 \times 10^{11} m\) away?
40. Distances in space are often quoted in units of light years, the distance light travels in one year.
(a) How many meters is a light year?
(b) How many meters is it to Andromeda, the nearest large galaxy, given that it is \(\displaystyle 2.00 \times 10^{6}\) light years away?
(c) The most distant galaxy yet discovered is \(\displaystyle 12.0 \times 10^{9}\) light years away. How far is this in meters?
41. A certain 50.0-Hz AC power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m.
(a) What is the wavelength of this very low frequency electromagnetic wave?
(b) What is its maximum magnetic field strength?
Solution
(a) \(\displaystyle 6.00 \times 10^{6} m\)
(b) \(\displaystyle 4.33 \times 10^{-5} T\)
42. During normal beating, the heart creates a maximum 4.00-mV potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave.
(a) What is the maximum electric field strength created?
(b) What is the corresponding maximum magnetic field strength in the electromagnetic wave?
(c) What is the wavelength of the electromagnetic wave?
43. (a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength (\(\displaystyle \lambda / 4 \) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band?
(b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.
Solution
(a) \(\displaystyle 1.50 \times 10^{6} Hz\), AM band
(b) The resonance of currents on an antenna that is 1/4 their wavelength is analogous to the fundamental resonant mode of an air column closed at one end, since the tube also has a length equal to 1/4 the wavelength of the fundamental oscillation.
44. (a) What is the wavelength of 100-MHz radio waves used in an MRI unit?
(b) If the frequencies are swept over a \(\displaystyle +/- 1.00\) range centered on 100 MHz, what is the range of wavelengths broadcast?
45. (a) What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery?
(b) Assuming the accuracy with which this EM radiation can ablate the cornea is directly proportional to wavelength, how much more accurate can this UV be than the shortest visible wavelength of light?
Solution
(a) \(\displaystyle 1.55 \times 10^{15} Hz\)
(b) The shortest wavelength of visible light is 380 nm, so that \[\frac{\lambda_{visible}}{\lambda_{UV}}\] \[= \frac{380 nm}{193 nm}\] \[= 1.97.\] In other words, the UV radiation is 97% more accurate than the shortest wavelength of visible light, or almost twice as accurate!
46. TV-reception antennas for VHF are constructed with cross wires supported at their centers, as shown in Figure 15 The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for particular channels and find them to be 1.94 and 0.753 m long, respectively. What are the frequencies for these channels?
A television reception antenna has cross wires of various lengths to most efficiently receive different wavelengths.
47. Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed back into sound on a speaker inside the astronaut’s space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut’s voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.60 s, what was the approximate distance to the Moon, neglecting any delays in the electronics?
Solution
\(\displaystyle 3.90 \times 10^{8} m\)
48. Lunar astronauts placed a reflector on the Moon’s surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time.
(a) To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns?
(b) What percent accuracy is this, given the average distance to the Moon is \(\displaystyle 3.84 \times 10^{8} m\)?
49. Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object.
(a) How far away is the planet Venus if the echo time is 1000 s?
(b) What is the echo time for a car 75.0 m from a Highway Police radar unit?
(c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 10.0 m?
Solution
(a) \(\displaystyle 1.50 \times 10^{11} m\)
(b) \(\displaystyle 0.500 \mu s\)
(c) 66.7 ns
50. Integrated Concepts:
(a) Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm.
(b) Compare this with the ratio of highest to lowest frequencies the ear can hear.
51. Integrated Concepts:
(a) Calculate the rate in watts at which heat transfer through radiation occurs (almost entirely in the infrared) from \(\displaystyle 1.0 m^{2}\) of the Earth’s surface at night. Assume the emissivity is 0.90, the temperature of the Earth is \(\displaystyle 15^{\circ}C\), and that of outer space is 2.7 K.
(b) Compare the intensity of this radiation with that coming to the Earth from the Sun during the day, which averages about \(\displaystyle 800 W/m^{2}\), only half of which is absorbed.
(c) What is the maximum magnetic field strength in the outgoing radiation, assuming it is a continuous wave?
Solution
(a) \(\displaystyle -3.5 \times 10^{2} W/m^{2}\)
(b) 88%
(c) \(\displaystyle 1.7 \mu T\)
24.4: Energy in Electromagnetic Waves
52. What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m?
Solution
\(\displaystyle I = \frac{c \epsilon_{0} E_{0}^{2}}{2}\)
\(\displaystyle = \frac{\left( 3.00 \times 10^{8} m/s \right) \left( 8.85 \times 10^{-12} C^{2} / N \cdot m^{2} \right) \left(125 V/m \right) ^{2}}{2}\)
\(\displaystyle = 20.7 W/m^{2}\)
53. Find the intensity of an electromagnetic wave having a peak magnetic field strength of \(\displaystyle 4.00 \times 10^{-9} T\).
54. Assume the helium-neon lasers commonly used in student physics laboratories have power outputs of 0.250 mW.
(a) If such a laser beam is projected onto a circular spot 1.00 mm in diameter, what is its intensity?
(b) Find the peak magnetic field strength.
(c) Find the peak electric field strength.
Solution
(a) \(\displaystyle I = \frac{P}{A} = \frac{P}{\pi r^{2}} = \frac{0.250 \times 10^{-3} W}{ \pi \left( 0.500 \times 10^{-3} m \right) ^{2}} = 318 W/m^{2}\)
\(\displaystyle I_{ave} = \frac{c B_{0}^{2}}{2 \mu_{0}} \rightarrow B_{0} = \left( \frac{2 \mu_{0}}{c}\right)^{1/2}\)
(b) \(\displaystyle = \left( \frac{2 \left(2 \pi \times 10^{-7} T \cdot m/A \right) \left( 318.3 W/m^{2} \right)}{ 3.00 \times 10^{8} m/s} \right) ^{1/2} \)
\(\displaystyle = 1.63 \times 10^{-6} T\)
(c) \(\displaystyle E_{0} = c B_{0} = \left( 3.00 \times 10^{8} m/s \right) \left(1.633 \times 10^{-6} T \right)\)
\(\displaystyle = 4.90 \times 10^{2} V/m\)
55. An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions.
(a) Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 30.0 km away? (Hint: Half the power will be spread over the area of a hemisphere.)
(b) What is the maximum electric field strength at this distance?
56. Suppose the maximum safe intensity of microwaves for human exposure is taken to be \(\displaystyle 1.00 W/m^{2}\).
(a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection.
(b) What is the maximum electric field strength at the safe intensity? (Note that early radar units leaked more than modern ones do. This caused identifiable health problems, such as cataracts, for people who worked near them.)
Solution
(a) 89.2 cm
(b) 27.4 V/m
57. A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of \(\displaystyle 7.50 \mu V/m\). (See the figure.) (a) What is the intensity of this wave? (b) What is the power received by the antenna? (c) If the orbiting satellite broadcasts uniformly over an area of \(\displaystyle 1.50 \times 10^{13} m^{2}\) (a large fraction of North America), how much power does it radiate?
Satellite dishes receive TV signals sent from orbit. Although the signals are quite weak, the receiver can detect them by being tuned to resonate at their frequency.
58. Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time -- called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of \(\displaystyle 1.00 \times 10^{11} V/m\) for a time of 1.00 ns.
(a) What is the maximum magnetic field strength in the wave?
(b) What is the intensity of the beam?
(c) What energy does it deliver on a \(\displaystyle 1.00 - mm^{2}\) area?
Solution
(a) 333 T
(b) \(\displaystyle 1.33 \times 10^{19} W/m^{2}\)
(c) 13.3 kJ
59. Show that for a continuous sinusoidal electromagnetic wave, the peak intensity is twice the average intensity (\(\displaystyle I_{0} = 2I_{ave}\)), using either the fact that \(\displaystyle E_{0} = \sqrt{2}E_{rms}\), or \(\displaystyle B_{0} = \sqrt{2}B_{rms}\), where rms means average (actually root mean square, a type of average).
60. Suppose a source of electromagnetic waves radiates uniformly in all directions in empty space where there are no absorption or interference effects.
(a) Show that the intensity is inversely proportional to \(\displaystyle r^{2}\), the distance from the source squared.
(b) Show that the magnitudes of the electric and magnetic fields are inversely proportional to \(\displaystyle r\).
Solution
(a) \(\displaystyle I = \frac{P}{A} = \frac{P}{4 \pi r^{2}} \propto \frac{1}{r^{2}}\)
(b) \(\displaystyle I \propto E_{0}^{2}, B_{0}^{2} \rightarrow E_{0}^{2}, B_{0}^{2} \propto \frac{1}{r^{2}} \rightarrow E_{0}, B_{0} \propto \frac{1}{r}\)
61. Integrated Concepts
An \(\displaystyle LC\) circuit with a 5.00-pF capacitor oscillates in such a manner as to radiate at a wavelength of 3.30 m.
(a) What is the resonant frequency?
(b) What inductance is in series with the capacitor?
62. Integrated Concepts
What capacitance is needed in series with an \(\displaystyle 800 - \mu H\) inductor to form a circuit that radiates a wavelength of 196 m?
Solution
13.5 pF
63. Integrated Concepts
Police radar determines the speed of motor vehicles using the same Doppler-shift technique employed for ultrasound in medical diagnostics. Beats are produced by mixing the double Doppler-shifted echo with the original frequency. If \(\displaystyle 1.50 \times 10^{9} - Hz\) microwaves are used and a beat frequency of 150 Hz is produced, what is the speed of the vehicle? (Assume the same Doppler-shift formulas are valid with the speed of sound replaced by the speed of light.)
64. Integrated Concepts:
Assume the mostly infrared radiation from a heat lamp acts like a continuous wave with wavelength \(\displaystyle 1.50 \mu m\).
(a) If the lamp’s 200-W output is focused on a person’s shoulder, over a circular area 25.0 cm in diameter, what is the intensity in \(\displaystyle W/m^{12}\)?
(b) What is the peak electric field strength?
(c) Find the peak magnetic field strength.
(d) How long will it take to increase the temperature of the 4.00-kg shoulder by \(\displaystyle 2.00^{\circ}C\), assuming no other heat transfer and given that its specific heat is \(\displaystyle 3.47 \times 10^{3} J/kg \cdot ^{\circ}C\)?
Solution
(a) \(\displaystyle 4.07 kW/m^{2}\)
(b) 1.75 kV/m
(c) \(\displaystyle 5.84 \mu T\)
(d) 2 min 19 s
65. Integrated Concepts:
On its highest power setting, a microwave oven increases the temperature of 0.400 kg of spaghetti by \(\displaystyle 45.0^{\circ}C\) in 120 s.
(a) What was the rate of power absorption by the spaghetti, given that its specific heat is \(\displaystyle 3.76 \times 10^{3} J/kg \cdot ^{\circ}C\)?
(b) Find the average intensity of the microwaves, given that they are absorbed over a circular area 20.0 cm in diameter.
(c) What is the peak electric field strength of the microwave? (d) What is its peak magnetic field strength?
66. Integrated Concepts:
Electromagnetic radiation from a 5.00-mW laser is concentrated on a \(\displaystyle 1.00 - mm^{2}\) area.
(a) What is the intensity in \(\displaystyle W/ m^{2}\)?
(b) Suppose a 2.00-nC static charge is in the beam. What is the maximum electric force it experiences?
(c) If the static charge moves at 400 m/s, what maximum magnetic force can it feel?
Solution
(a) \(\displaystyle 5.00 \times 10^{3} W/m^{2}\)
(b) \(\displaystyle 3.88 \times 10^{-6} N\)
(c)\(\displaystyle 5.18 \times 10^{-12} N\)
67. Integrated Concepts:
A 200-turn flat coil of wire 30.0 cm in diameter acts as an antenna for FM radio at a frequency of 100 MHz. The magnetic field of the incoming electromagnetic wave is perpendicular to the coil and has a maximum strength of \(\displaystyle 1.00 \times 10^{-12} T\).
(a) What power is incident on the coil?
(b) What average emf is induced in the coil over one-fourth of a cycle?
(c) If the radio receiver has an inductance of \(\displaystyle 2.50 \mu H\), what capacitance must it have to resonate at 100 MHz?
68. Integrated Concepts:
If electric and magnetic field strengths vary sinusoidally in time, being zero at \(\displaystyle t = 0\), then \(\displaystyle E = E_{0} \sin{2 \pi} ft\) and \(\displaystyle B = B_{0} \sin{2 \pi} ft\). Let \(\displaystyle f = 1.00 GHz\) here.
(a) When are the field strengths first zero?
(b) When do they reach their most negative value?
(c) How much time is needed for them to complete one cycle?
Solution
(a) \(\displaystyle t = 0\)
(b) \(\displaystyle 7.50 \times 10^{-10} s\)
(c) \(\displaystyle 1.00 \times 10^{-9} s\)
69. Unreasonable Results:
A researcher measures the wavelength of a 1.20-GHz electromagnetic wave to be 0.500 m.
(a) Calculate the speed at which this wave propagates.
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
70. Unreasonable Results:
The peak magnetic field strength in a residential microwave oven is \(\displaystyle 9.20 \times 10^{-5} T\).
(a) What is the intensity of the microwave?
(b) What is unreasonable about this result?
(c) What is wrong about the premise?
Solution
(a) \(\displaystyle 1.01 \times 10^{6} W/m^{2}\)
(b) Much too great for an oven.
(c) The assumed magnetic field is unreasonably large.
71. Unreasonable Results:
An \(\displaystyle LC\) circuit containing a 2.00-H inductor oscillates at such a frequency that it radiates at a 1.00-m wavelength.
(a) What is the capacitance of the circuit?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
72. Unreasonable Results:
An \(\displaystyle LC\) circuit containing a 1.00-pF capacitor oscillates at such a frequency that it radiates at a 300-nm wavelength.
(a) What is the inductance of the circuit?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
Solution
(a) \(\displaystyle 2.53 \times 10^{-20} H\)
(b) L is much too small.
(c) The wavelength is unreasonably small.
73. Create Your Own Problem:
Consider electromagnetic fields produced by high voltage power lines. Construct a problem in which you calculate the intensity of this electromagnetic radiation in \(\displaystyle W/m^{2}\) based on the measured magnetic field strength of the radiation in a home near the power lines. Assume these magnetic field strengths are known to average less than a \(\displaystyle \mu T\). The intensity is small enough that it is difficult to imagine mechanisms for biological damage due to it. Discuss how much energy may be radiating from a section of power line several hundred meters long and compare this to the power likely to be carried by the lines. An idea of how much power this is can be obtained by calculating the approximate current responsible for \(\displaystyle \mu T\) fields at distances of tens of meters.
74.  Construct a problem in which you calculate the power received by the dish and the maximum electric field strength of the microwave signals for a single channel received by the dish. Among the things to be considered are the power broadcast by the satellite and the area over which the power is spread, as well as the area of the receiving dish.
Contributors and Attributions
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Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0) .


3.2: Minor Key Signatures
Minor key signatures agree with the notes of the natural minor scale. Since the CC natural minor scale had EE♭, AA♭, and BB♭, the key signature of C minor has three flats, written in the order of flats—BB♭, EE♭, AA♭.
Therefore, a minor key signature will have three lowered notes—the 3rd, 6th, and 7th—in relation to the corresponding major key signature. We use the term parallel minor when referring to a minor scale that has the same 1st scale degree (in this case CC) as the major. We say, “The parallel minor of EE major is EE minor,” and “The parallel major of FF minor is FF major.” One method of figuring out a minor key signature is to add three flats to the parallel major key signature. This is the same as subtracting three sharps.
Note on uppercase versus lowercase: When writing below the five-line staff to designate keys, we will use the shorthand of upper case for major (CC) and lowercase for minor (cc). When writing prose, we will use uppercase: C major and C minor.
We use the term relative minor when referring to a minor key that has the same key signature as a major key. For example, the relative minor of EE♭ major is CCminor because both have three flats in the key signature. Conversely, one could say the relative major of CC minor is EE♭ major. The relative major is three half steps above the relative minor.
Below are the minor key signatures.
Here are circle of fifths diagrams for both major and minor, for comparison.
Writing harmonic minor and melodic minor scales when using minor key signatures requires you to raise scale degrees.
Compositions in minor typically do not strictly use only one of the three minor scales, however. The three minor scales are distillations of composers’ actual practice.


10.2: Principles of Communication Climate
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In this section we will discuss the five principles of communication climate: messages contain relational subtexts that can be felt; climate is conveyed through words, action, and non-action; climate is perceived; climate is determined by social and relational needs; and relational messages are multi-leveled.
Messages contain relational subtexts that can be felt
In addition to generating and perceiving meaning in communicative interactions, we also subtly (and sometimes not so subtly) convey and perceive the way we feel about each other. As we discussed in Chapter 1: Introduction to Communication, almost all messages operate on two levels: content and relational. As a reminder, the content is the substance of what’s being communicated (the what of the message). The relational dimension isn’t the actual thing being discussed and instead can reveal something about the relational dynamic existing between you and the other person (the who of the message). We can think of it as a kind of subtext, an underlying (or hidden) message that says something about how the parties feel toward one another. For example, when deciding on a TV program, your partner might politely suggest, “I’d like to watch this show, how about you?” The content of the message is about what they want to watch. The relational subtext is subtle but suggests your partner values your input and wants to share decision-making control. The climate of this interaction is likely to be neutral or warm. However, consider how the relational subtext changes if your partners insists (with a raised voice and a glare): “We are WATCHING THIS SHOW tonight!” The content is still about what they want to watch. But what is the subtext now? In addition to what your partner wants to watch, they seem to be sending a relational message of dominance, control and potential disrespect for your needs and wants. You might be hearing an additional message of “I don’t care about you,” which is likely to feel cold, eliciting a negative emotional reaction such as defensiveness or sadness.
Climate is conveyed through words, action, and non-action
Relational subtexts can be conveyed through direct words and actions. A student making a complaint to an instructor can be worded with respect, as in “Would you have a few minutes after class to discuss my grade?” or without, as in “I can’t believe you gave me such a crappy grade, and we need to talk about it right after class!” We can often find more of the relational meaning in the accompanying and more indirect nonverbals—in the way something is said or done. For example, two of your coworkers might use the exact same words to make a request of you, but the tone, emphasis, and facial expression will change the relational meaning, which influences the way you feel. The words “can you get this done by Friday” will convey different levels of respect and control depending upon the nonverbal emphasis, tone, and facial expressions paired with the verbal message. For example, the request can be made in a questioning tone versus a frustrated or condescending one. Additionally, a relational subtext might also be perceived by what is NOT said or done. For example, one coworker adds a “thanks” or a “please” and the other doesn’t. Or, one coworker shows up to your birthday coffee meetup and the other doesn’t. What do these non-actions suggest to you about the other person’s feelings or attitude towards you? Consider for a moment some past messages (and non-messages) that felt warm or cold to you.
Climate is perceived
Relational meanings are not inherent in the messages themselves. They are not literal, and they are not facts. The subtext of any communicative message is in the eye of the beholder. The relational meaning can be received in ways that were unintentional. Additionally, like content messages, relational messages can be influenced by what we attend to and by our expectations (as discussed in Chapter 3: The Perception Process and Perception of Others). They also stand out more if they contrast with what you normally expect or prefer.
You might interpret your partner’s insistence on watching a certain show to mean they are bossy. However, your partner might have perceived you to be the bossy one and is attempting to regain loss of decision control. Control could be exerted because doing so is the accepted relational dynamic between you, or it could be a frustrated reaction to a frequent loss of decision control, which they want to regain. Here, it needs to be noted that the relational message someone hears at any given time is a perception and doesn’t necessarily mean the message received was the message intended. Meanings will depend on who is delivering it and in what context. Cultural and co-cultural context will also impact the way a message is interpreted, which we will discuss later in the Communication Competence section of this chapter. In addition, later in this chapter we will discuss metacommunication, a way to address climate and relational subtexts in interactions in order to clarify intent and increase shared meaning.
Climate is determined by social and relational needs
While relational messages can potentially show up in dozens of different communicative forms, they generally fall into categories that align with specific types of human social needs that vary from person to person and situation to situation. In addition to physical needs, such as food and water, human beings have social and relational needs that can have negative consequences if ignored. Negative consequences can range from frustrating work days to actual death (in cases of infants not getting human touch and attention and the elderly who suffer in isolation). Scholars categorize social needs in many different ways. Recall the discussion of Interpersonal Needs Theory from Chapter 8: Interpersonal Relationships, which explained that we are more likely to develop relationships with people who meet one or more of three basic interpersonal needs: affection, control, and belonging. We want to be liked or loved. We want to be able to influence others and our own environments (at least somewhat). We want to feel included. Each need exists on a continuum from low to high, with some people needing only a little of one and more of another. The level of need also varies by context, with some situations calling for more affection (e.g., romantic relationships) and others calling for less (e.g., workplace).
Another framework for categorizing needs comes from a nonviolent communication approach used by mediators, negotiators, therapists, and businesses across the world. This approach focuses on compassion and collaboration and categorizes human needs with more detail and scope. For example, categories include freedom, connection, community, play, integrity, honesty, peace, and the needs to matter and be understood. When people from all cultures and all walks of life all over the world are asked “Do you need these to thrive?” the answer—with small nuances—is always “yes” (Sofer, 2018).
During interactions, we detect on some level whether the person with whom we are communicating is meeting a particular need, such as the need for respect. We may not really be aware, on a conscious level, of why we feel cold toward a coworker. But, it is likely that the coworker’s jokes, eyerolls, and criticisms toward you feel like a relational message of inferiority or disrespect. In this case, your unmet need for dignity, competence, respect or belonging may be contributing to your cold reaction toward this person. When other people’s messages don’t meet our needs in whole or in part, we tend to have an emotionally cold reaction. When messages do meet our needs, we tend to feel warm.
Consider how needs may be met (or not met) in when you are in a disagreement of opinion with someone else. For example, needs may be met if we feel heard by the other and not met if we feel disrespected when we present our opinion. In a different example, consider all the different ways you could request that someone turn the music down. You could do both of these things with undertones (relational subtexts) of superiority, anger, dominance, ridicule, coldness, distance, etc. Or you could do them with warmth, equality, playfulness, shared control, respect, trust, etc.
Relational messages are multi-leveled
On one level, we want to feel that our social needs are met and we hope that others in our lives will meet them through their communication, at least in part. On another level, though, we are concerned with how we are perceived; the self-image we convey to others is important to us. We want it to be apparent to others that we belong, matter, are respected, understood, competent, and in control of ourselves. Some messages carry relational subtexts that harm or threaten our self-image, while others confirm and validate it.
To help better understand this second level of relational subtexts, let’s discuss the concept of “face needs.” Face refers to our self-image when communicating with others (Ting-Toomey, 2005; Brown and Levinson, 1987; Lim and Bowers, 1991). It does not refer to our physical face, but more of an unsaid portrayal of the image that we want to project to others, and sometimes even to ourselves. Most of us are probably unaware of the fact that we are frequently negotiating this face as we interact with others. However, on some level, whether we are aware of it or not, many of our social needs relate to the way we want to be perceived by others. Specifically, we not only want to feel included in particular groups, we also want to be seen as someone who belongs. We want to feel capable and competent, but we also want others to think we are capable and competent. We want to experience a certain level of autonomy, but we also want to be seen as free from the imposition of others. Communication subtexts such as disrespect tend to threaten our face needs, while other behaviors such as the right amount of recognition support them. Once again, we can apply the temperature analogy here. When we perceive our “face” to be threatened, we may feel cold. When our face needs are honored, we may feel warm. Effective communication sometimes requires a delicate dance that involves addressing, maintaining, and restoring our own face and that of others simultaneously.
Because both our own needs and the needs of others play an important role in communication climate, throughout the rest of this chapter we will utilize the following three general categories when we refer to social needs that can be addressed through communication:
- Need for Connection: belonging, inclusion, acceptance, warmth, kindness
- Need for Freedom: autonomy, control, freedom from imposition by others, space, privacy
- Need for Meaning: competence, capability, dignity, worthiness, respect, to matter, to be understood


1.7: Conventional Versus Electron Flow
Positive and Negative Electron Charge
When Benjamin Franklin made his conjecture regarding the direction of charge flow (from the smooth wax to the rough wool), he set a precedent for electrical notation that exists to this day, despite the fact that we know electrons are the constituent units of charge, and that they are displaced from the wool to the wax—not from the wax to the wool—when those two substances are rubbed together. This is why electrons are said to have a negative charge: because Franklin assumed electric charge moved in the opposite direction that it actually does, and so objects he called “negative” (representing a deficiency of charge) actually have a surplus of electrons.
By the time the true direction of electron flow was discovered, the nomenclature of “positive” and “negative” had already been so well established in the scientific community that no effort was made to change it, although calling electrons “positive” would make more sense in referring to “excess” charge. You see, the terms “positive” and “negative” are human inventions, and as such have no absolute meaning beyond our own conventions of language and scientific description. Franklin could have just as easily referred to a surplus of charge as “black” and a deficiency as “white,” in which case scientists would speak of electrons having a “white” charge (assuming the same incorrect conjecture of charge position between wax and wool).
Conventional Flow Notation
However, because we tend to associate the word “positive” with “surplus” and “negative” with “deficiency,” the standard label for electron charge does seem backward. Because of this, many engineers decided to retain the old concept of electricity with “positive” referring to a surplus of charge, and label charge flow (current) accordingly. This became known as conventional flow notation:
Electron Flow Notation
Others chose to designate charge flow according to the actual motion of electrons in a circuit. This form of symbology became known as electron flow notation:
In conventional flow notation, we show the motion of charge according to the (technically incorrect) labels of + and -. This way the labels make sense, but the direction of charge flow is incorrect. In electron flow notation, we follow the actual motion of electrons in the circuit, but the + and - labels seem backward. Does it matter, really, how we designate charge flow in a circuit? Not really, so long as we’re consistent in the use of our symbols. You may follow an imagined direction of current (conventional flow) or the actual (electron flow) with equal success insofar as circuit analysis is concerned. Concepts of voltage, current, resistance, continuity, and even mathematical treatments such as Ohm’s Law (chapter 2) and Kirchhoff’s Laws (chapter 6) remain just as valid with either style of notation.
Conventional Flow Notation vs Electron Flow Notation
You will find conventional flow notation followed by most electrical engineers, and illustrated in most engineering textbooks. Electron flow is most often seen in introductory textbooks (this one included) and in the writings of professional scientists, especially solid-state physicists who are concerned with the actual motion of electrons in substances. These preferences are cultural, in the sense that certain groups of people have found it advantageous to envision electric current motion in certain ways. Being that most analyses of electric circuits do not depend on a technically accurate depiction of charge flow, the choice between conventional flow notation and electron flow notation is arbitrary . . . almost.
Polarization and Nonpolarization
Many electrical devices tolerate real currents of either direction with no difference in operation. Incandescent lamps (the type utilizing a thin metal filament that glows white-hot with sufficient current), for example, produce light with equal efficiency regardless of current direction. They even function well on alternating current (AC), where the direction changes rapidly over time. Conductors and switches operate irrespective of current direction, as well. The technical term for this irrelevance of charge flow is nonpolarization . We could say then, that incandescent lamps, switches, and wires are nonpolarized components. Conversely, any device that functions differently on currents of different direction would be called a polarized device.
There are many such polarized devices used in electric circuits. Most of them are made of so-called semiconductor substances, and as such aren’t examined in detail until the third volume of this book series. Like switches, lamps, and batteries, each of these devices is represented in a schematic diagram by a unique symbol. As one might guess, polarized device symbols typically contain an arrow within them, somewhere, to designate a preferred or exclusive direction of current. This is where the competing notations of conventional and electron flow really matter. Because engineers from long ago have settled on conventional flow as their “culture’s” standard notation, and because engineers are the same people who invent electrical devices and the symbols representing them, the arrows used in these devices’ symbols all point in the direction of conventional flow, not electron flow . That is to say, all of these devices’ symbols have arrow marks that point against the actual flow of electrons through them.
Perhaps the best example of a polarized device is the diode . A diode is a one-way “valve” for electric current, analogous to a check valve for those familiar with plumbing and hydraulic systems. Ideally, a diode provides unimpeded flow for current in one direction (little or no resistance), but prevents flow in the other direction (infinite resistance). Its schematic symbol looks like this:
Placed within a battery/lamp circuit, its operation is as such:
When the diode is facing in the proper direction to permit current, the lamp glows. Otherwise, the diode blocks all electron flow just like a break in the circuit, and the lamp will not glow.
If we label the circuit current using conventional flow notation, the arrow symbol of the diode makes perfect sense: the triangular arrowhead points in the direction of charge flow, from positive to negative:
On the other hand, if we use electron flow notation to show the true direction of electron travel around the circuit, the diode’s arrow symbology seems backward:
For this reason alone, many people choose to make conventional flow their notation of choice when drawing the direction of charge motion in a circuit. If for no other reason, the symbols associated with semiconductor components like diodes make more sense this way. However, others choose to show the true direction of electron travel so as to avoid having to tell themselves, “just remember the electrons are actually moving the other way” whenever the true direction of electron motion becomes an issue.
Which One Should You Use?
In this series of textbooks, I have committed to using electron flow notation. Ironically, this was not my first choice. I found it much easier when I was first learning electronics to use conventional flow notation, primarily because of the directions of semiconductor device symbol arrows. Later, when I began my first formal training in electronics, my instructor insisted on using electron flow notation in his lectures. In fact, he asked that we take our textbooks (which were illustrated using conventional flow notation) and use our pens to change the directions of all the current arrows so as to point the “correct” way! His preference was not arbitrary, though. In his 20-year career as a U.S. Navy electronics technician, he worked on a lot of vacuum-tube equipment. Before the advent of semiconductor components like transistors, devices known as vacuum tubes or electron tubes were used to amplify small electrical signals. These devices work on the phenomenon of electrons hurtling through a vacuum, their rate of flow controlled by voltages applied between metal plates and grids placed within their path, and are best understood when visualized using electron flow notation.
When I graduated from that training program, I went back to my old habit of conventional flow notation, primarily for the sake of minimizing confusion with component symbols, since vacuum tubes are all but obsolete except in special applications. Collecting notes for the writing of this book, I had full intention of illustrating it using conventional flow.
Years later, when I became a teacher of electronics, the curriculum for the program I was going to teach had already been established around the notation of electron flow. Oddly enough, this was due in part to the legacy of my first electronics instructor (the 20-year Navy veteran), but that’s another story entirely! Not wanting to confuse students by teaching “differently” from the other instructors, I had to overcome my habit and get used to visualizing electron flow instead of conventional. Because I wanted my book to be a useful resource for my students, I begrudgingly changed plans and illustrated it with all the arrows pointing the “correct” way. Oh well, sometimes you just can’t win!
On a positive note (no pun intended), I have subsequently discovered that some students prefer electron flow notation when first learning about the behavior of semiconductive substances. Also, the habit of visualizing electrons flowing against the arrows of polarized device symbols isn’t that difficult to learn, and in the end I’ve found that I can follow the operation of a circuit equally well using either mode of notation. Still, I sometimes wonder if it would all be much easier if we went back to the source of the confusion—Ben Franklin’s errant conjecture—and fixed the problem there, calling electrons “positive” and protons “negative.”


5.6: Watermarks
Learning Objectives
- Insert a watermark.
Text Watermark
You can add a watermark to documents in Word by going to Design>Watermark. (In older versions of Word, it is often found in the Page Layout tab rather than the Design tab.)
Choosing a watermark from the menu will apply it to every page in the document.
To change the text of the watermark, click Custom Watermark.. . at the bottom of the Watermark menu to open the Printed Watermark dialog box.
Here, you can customize the text and appearance of the watermark. Unchecking the semitransparent box will make the watermark more visible (although the watermark will still not obscure the text).
Practice Question
Picture Watermark
To add an image as a watermark, go to Design>Watermark>Custom watermark… and select the Picture watermark in the Printed Watermark dialog box.
Click Select Picture… and then Browse to choose an image on your computer. Uncheck the Washout box if you want a darker, more visible watermark. Then click OK in the Printed Watermark dialog box.
Contributors and Attributions
- Tree [used in watermark]. Authored by : Edward Boatman. Located at : https://thenounproject.com/term/tree/459/ . License : CC BY: Attribution
- Watermarks. Authored by : Lumen Learning. License : CC BY: Attribution


3.1: Navigating Microsoft Word
By the end of this section, you will be able to:
- Identify the most commonly used tabs in Microsoft Word
- Use the Navigation pane
Microsoft Word is a sophisticated word processing application. It completely transformed the document-creation process, replacing typewriters and existing word processing programs, such as WordPerfect and WordStar, with a user-friendly digital interface and hundreds of options for formatting. The comprehensive features allow users to easily adjust fonts and page layouts, insert graphics, track revisions, communicate collaboratively via comments, check spelling, search for text, and much more.
Let’s get started on our market trends report. As you learned in the chapter on Essentials of Software Applications for Business, you should first open a new, blank document in Word. Using the default settings, type the following into the document:
Industry and Market Analysis
The laptop industry is growing at a rather slow rate with sales expected to grow around 1% annually. Sales in the industry currently are over $20 billion. A large part of sales comes from consumer demand. There are several key players in the laptop industry. The largest companies in the industry in terms of consumer laptop ownership in the United States (market share) are HP, Dell, Apple, Acer, and Lenovo. Individuals can purchase a laptop at various price points based on the features, speed, and storage capabilities of the laptop. These companies also compete in the tablet industry and some consumers might make the decision to choose a tablet over a laptop. There are also laptops that are considered “convertible,” meaning that they can be more like a tablet or a laptop with the screen feature that allows full rotation.
You will use this text to build the framework for the market trends report as you move through the sections in this chapter and in subsequent chapters.
Tabs
Word comes with a set of default tabs (or menus), which are the interface for most of the functions and features you will use. Those tabs are File, Home, Insert, Draw, Design, Layout, References, Mailings, Review, View, and Help.
These same tabs are on the Mac Menu Bar, but the menu bar varies when you are in Word. There is no File tab on Word’s toolbar in Mac. The default tabs you see depend on the settings you have selected. They usually are Home, Insert, Draw, Design, Layout, References, Mailings, Review, View, and Tell Me. You can access Word preferences and settings via the taskbar at the top of the screen.
Many of the features that are common among the tabs in Office were covered in the Essentials of Software Applications for Business chapter. In this chapter, you will learn more about how the tabs work in Word.
You can customize your menu bar by adding or hiding tabs, and by modifying the tools that appear on each tab. There are hundreds of commands you can choose from; the Word interface is highly customizable. Customization of the tabs was covered in the chapter on Essentials of Software Applications for Business. The next sections introduce some of the most important default tabs and their overall function, as well as the most-used commands, as Figure 3.2 shows.
Home Tab
The Home tab is where you will spend most of your time, as it contains the formatting of fonts, alignment, headings, numbering, and lists, as well as the Find commands. It is also the default tab that displays when you open your document. We will go over the Home tab commands in detail in Formatting Document Layout in Microsoft Word.
Insert Tab
The Insert tab is useful for adding certain material into your document. The Insert tab also allows the user to include elements such as headers and footers, page numbers, page breaks, and bookmarks. We will review using these features in more detail in the chapter on Document Preparation.
Knowing how to use the Insert tab is particularly important for designing business documents, such as your WorldCorp market trends report. Your report will contain many pages and sections, as well as a table of contents and page numbers. It will also likely contain charts, graphs, and images, all of which need to be inserted into the document. For example, you could insert a chart of the top-selling TV screens (by using the Charts drop-down menu), then add a callout or label explaining the chart (by using the Shapes drop-down menu).
Layout Tab
The Layout tab is where you will configure your page setup. It includes commands for adjusting margins and the paper size, as well as options for shaping the text on the page with columns. The Paragraph command group is for adjusting the alignment of lists, body text, and objects such as pictures in your document. This tab also gives the user options for adding page breaks and line numbers.
Review Tab
If you are working with a team on your documents, you’ll likely use the Review tab . This tab has a commenting function that allows users to add comments to a file, and to respond to each other’s comments, as also discussed in the Essentials of Software Applications for Business chapter. As Figure 3.3 shows, the Review tab contains the Track Changes feature, which is helpful when many people are taking turns reviewing and contributing to a document. When Track Changes is turned on, edits to the document appear underlined and in colored text. Each user’s edits will be colored differently to easily distinguish input from multiple people. This is particularly helpful when documents go through several revisions and are reviewed by many people. The market trends report for WorldCorp is a team effort, requiring several people to contribute to the final product. You can expect that as the document is created and revised, comments will be used to help reach the final version of the report.
The Track Changes process might feel familiar to you, as it is designed to mimic the act of marking up a paper document with a pen. You might have had someone work on your résumé or mark up a homework assignment of yours, using a red pen to make suggestions and revisions on the document itself. In a Word document, comments and Track Changes serve the same purpose as using a red pen on a paper document. This process will be covered in more detail later in the chapter.
The Review tab also has many commands that allow commenting and suggesting changes in documents that are used and edited by multiple people. Figure 3.3 shows two comments that users made by choosing the New Comment function. As people work on the document, they can read and respond to those comments, or remove them by clicking on them and selecting Delete in the Comments menu. There are also options in the Show Markup button found in the Tracking command group to display (or not display) formatting changes such as boldfacing or underlining.
Also on the Review tab, the Proofing command group contains helpful tools that you will use often when writing and editing a document. You can check your spelling and grammar, look up words in a dictionary or thesaurus, and keep track of your word count.
You will learn more about the Review tab and its features in Formatting Document Layout in Microsoft Word.
View Tab
The View tab is useful for changing how you see your document. For instance, it gives you the option of looking at your document one or two pages at time. You can also activate the zoom option from here, as well as add rulers and gridlines, which are helpful when placing objects, such as a table or picture, in the report you may be writing. You can also access the Navigation pane in the View tab. You may also use the read, print, or web viewing modes when typing, which give you different ways of seeing your document, as Figure 3.4 shows.
Navigation Pane
The Navigation pane serves various purposes. The Navigation pane is accessed directly by checking the box on the View tab in the Show command group. You can also get the Navigation pane by selecting Find from the Home tab. With either of these options, a pane will open on the left side of the screen. There are three tabs in the Navigation pane: Headings, Pages, and Results. The first tab, Headings, is the first thing you will see when you open the Navigation pane. This tab shows the outline of your document, but only if you have placed headings for each section and subsection (which you will learn more about in the section on Formatting Document Content in Microsoft Word). The Pages tab shows a thumbnail representation of the pages of the document. The Results tab is used for searching for a particular word, phrase, or number throughout the document, as Figure 3.5 shows. You can always activate the Find function with the Ctrl+F keyboard shortcut.
To activate the Find function on a Mac, press Command+F .
What Is a Document?
You will likely work in creating, editing, and consuming documents throughout your personal life and professional career. But what exactly is a document? Generally, a document is any type of file that contains information or transferred thoughts/ideas. While historically these documents were transferred to some type of paper or physical presentation on a chalkboard or displayed with an overhead projector, nowadays these are largely found in electronic format. However, when we are referring to a document with respect to Word, we are referring to a very specific type of file. This document file will contain primarily text and images that have been formatted and processed electronically. Hence, Word is a word processor, a type of program that contains a number of different text formatting capabilities for producing primarily text-based files and documents. This is an important distinction, as you can create any number of different text-based files in several different programs.
There will be times when you may not have access to Word or another word processing program. Many computers, and even some portable devices, will come with a preinstalled basic text processing as part of their operating system. Notepad is one example. While you will not be able to format the text (not even bold, italic, or underline), you can capture basic text information and save it as a basic text file (.txt) to your computer. This can be useful for jotting down quick notes—hence the name Notepad. Then, later, when you have access to Word, you can copy and paste the text from Notepad into Word, where you can format it and incorporate it into other documents if needed.


6.5: Emotional over-control, alienation, and psychological distancing
Shaping such an outward image requires emotional responses to be carefully measured. Thus, prisoners struggle to control and suppress their own internal emotional reactions to events around them. Emotional over-control and a generalized lack of spontaneity may occur as a result. Admissions of vulnerability to persons inside the immediate prison environment are potentially dangerous because they invite exploitation. As one experienced prison administrator once wrote: "Prison is a barely controlled jungle where the aggressive and the strong will exploit the weak, and the weak are dreadfully aware of it." Some prisoners are forced to become remarkably skilled "self-monitors" who calculate the anticipated effects that every aspect of their behavior might have on the rest of the prison population and strive to make such calculations second nature.
Prisoners who labor at both an emotional and behavioral level to develop a "prison mask" that is unrevealing and impenetrable risk alienation from themselves and others, may develop emotional flatness that becomes chronic and debilitating in social interaction and relationships, and find that they have created a permanent and unbridgeable distance between themselves and other people. Many for whom the mask becomes especially thick and effective in prison find that the disincentive against engaging in open communication with others that prevails there has led them to withdrawal from authentic social interactions altogether. The alienation and social distancing from others are a defense not only against exploitation but also against the realization that the lack of interpersonal control in the immediate prison environment makes emotional investments in relationships risky and unpredictable.


11.6C: Hypothalamus
The hypothalamus serves as a gateway between the nervous system and endocrine system.
- Describe the functions of the hypothalamus of the brain.
Key Points
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The hypothalamus produces and secretes a wide variety of neurohormones that lead to the release or inhibition of pituitary gland
hormone. - The posterior pituitary is composed of tissue derived from the hypothalamus, whereas the anterior pituitary is derived from epithelial tissue.
- The hypothalamus can pass signals back and forth between the anterior and posterior pituitary by the neurohypophysis and median eminence.
- The hypothalamus can sample the blood composition at two sites, the subfornical organ and the organum vasculosum of the lamina terminalis. This is important for the uptake of circulating hormones and to determine concentration of substances in the blood.
- The outputs of the hypothalamus can be divided into neural projections and endocrine hormones. The neural projections tend to run bidirectionally.
Key Terms
- neurohypophysis : The posterior lobe of the pituitary gland, responsible for the release of oxytocin and antidiuretic hormone (ADH), also called vasopressin.
- median eminence : Part of the inferior boundary for the hypothalamus and one of the seven areas of the brain devoid of a blood-brain barrier.
- anterior pituitary : Also called the adenohypophysis, the glandular anterior lobe of the pituitary gland. The anterior pituitary regulates several physiological processes including stress, growth, reproduction, and lactation.
The hypothalamus (derived from the Greek for “under chamber”) is a portion of the brain that contains a number of small, distinct nuclei with various functions and less anatomically distinct areas. The hypothalamus is located below the thalamus just above the brain stem. In the terminology of neuroanatomy, it forms the ventral part of the diencephalon. All vertebrate brains contain a hypothalamus. In humans, it is roughly the size of an almond.
The location of hypothalamus and pituitary : At center, hypothalamus is located just superior to the pituitary, with which it closely interacts.
General Functions
Location of the hypothalamus : This is the location of the human hypothalamus in relation to the thalamus, pituitary gland, sella turcica, and optic chiasm.
One of the most important functions of the hypothalamus is linking the nervous system to the endocrine system via the pituitary gland (hypophysis).
The hypothalamus contains thyrotropin-releasing hormone, gonadotropin-releasing hormone, growth hormone-releasing hormone, corticotropin-releasing hormone, somatostatin, and dopamine, as well as vasopressin and oxytocin. These hormones are released into the bloodstream and target other organ systems, most notably the pituitary.  Most of the hypothalamic hormones generated are distributed to the pituitary via the hypophyseal portal system. The hypothalamus maintains homeostasis, including the regulation of blood pressure, heart rate, and temperature.
The hypothalamus coordinates hormonal and behavioral circadian rhythms, complex patterns of neuroendocrine outputs, complex homeostatic mechanisms, and important behaviors. It must therefore respond to many different signals, some of which are generated externally and some internally. The hypothalamus is thus richly connected with many parts of the central nervous system, including the brainstem, reticular formation and autonomic zones, and the limbic forebrain (particularly the amygdala, septum, diagonal band of Broca, olfactory bulbs, and cerebral cortex).
The hypothalamus can sample the blood composition at the subfornical organ and the organum vasculosum of the lamina terminalis. This is important for the uptake of circulating hormones and to determine concentration of substances in the blood.
Temperature Regulation
The hypothalamus functions as a type of thermostat for the body. It sets a desired body temperature and stimulates either heat production and retention to raise the blood temperature to a higher level, or sweating and vasodilation to cool the blood to a lower temperature. All fevers result from a raised setting in the hypothalamus; elevated body temperatures due to any other cause are classified as hyperthermia. Rarely, direct damage to the hypothalamus such as from a stroke causes a fever; this is sometimes called a hypothalamic fever. However, such damage more commonly causes abnormally low body temperatures.
Appetite
The extreme lateral part of the ventromedial nucleus of the hypothalamus is responsible for control of food intake. Stimulation of this area causes increased food intake. Bilateral lesion in this area causes complete cessation of food intake. Medial parts of the nucleus have a controlling effect on the lateral part. Bilateral lesion of the medial part of the ventromedial nucleus causes hyperphagia and obesity. Further lesion of the lateral part of the ventromedial nucleus in the same animal produces complete cessation of food intake.
Fear Processing
The medial zone of hypothalamus is part of a circuitry that controls motivated behaviors, such as defensive behaviors and social defeat. Analyses of Fos-labeling showed that a series of nuclei in the behavioral control column is important in regulating the expression of innate and conditioned defensive behaviors. Nuclei in the medial zone are also mobilized during an encounter with an aggressor. The defeated animal has an increase in Fos levels in sexually dimorphic structures.
Sexual Dimorphism
Several hypothalamic nuclei are sexually dimorphic, with clear differences in both structure and function between males and females. Some differences are apparent even in gross neuroanatomy, most notably is the sexually dimorphic nucleus within the preoptic area. However, most are subtle changes in the connectivity and chemical sensitivity of particular sets of neurons. In neonatal life, gonadal steroids influence the development of the neuroendocrine hypothalamus. For instance, they determine the ability of females to exhibit a normal reproductive cycle and of males and females to display appropriate reproductive behaviors in adult life.
In 2004 and 2006, two studies by Berglund, Lindström, and Savic used Positron Emission Tomography (PET) to observe how the hypothalamus responds to smelling common odors, the scent of testosterone found in male sweat, and the scent of estrogen found in female urine. These studies showed that the hypothalamus of heterosexual men and homosexual women both respond to estrogen. Also, the hypothalamus of homosexual men and heterosexual women both respond to testosterone. In all four groups, common odors were processed similarly involving only the olfactory brain.


13.5: Inference for Linear Regression
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- Last updated
- Save as PDF
In this section we discuss uncertainty in the estimates of the slope and y-intercept for a regression line. Just as we identified standard errors for point estimates in previous chapters, we first discuss standard errors for these new estimates. However, in the case of regression, we will identify standard errors using statistical software.
Midterm elections and unemployment
Elections for members of the United States House of Representatives occur every two years, coinciding every four years with the U.S. Presidential election. The set of House elections occurring during the middle of a Presidential term are called midterm elections. In America's two-party system, one political theory suggests the higher the unemployment rate, the worse the President's party will do in the midterm elections.
To assess the validity of this claim, we can compile historical data and look for a connection. We consider every midterm election from 1898 to 2010, with the exception of those elections during the Great Depression. Figure \(\PageIndex{1}\) shows these data and the least-squares regression line:
\[\text {% change in House seats for President's party}\]
\[= -6.71 - 1.00 \times \text {(unemployment rate)}\]
We consider the percent change in the number of seats of the President's party (e.g. percent change in the number of seats for Democrats in 2010) against the unemployment rate.
Examining the data, there are no clear deviations from linearity, the constant variance condition, or in the normality of residuals (though we don't examine a normal probability plot here). While the data are collected sequentially, a separate analysis was used to check for any apparent correlation between successive observations; no such correlation was found.
Exercise \(\PageIndex{1}\)
The data for the Great Depression (1934 and 1938) were removed because the unemployment rate was 21% and 18%, respectively. Do you agree that they should be removed for this investigation? Why or why not?
- Answer
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We will provide two considerations. Each of these points would have very high leverage on any least-squares regression line, and years with such high unemployment may not help us understand what would happen in other years where the unemployment is only modestly high. On the other hand, these are exceptional cases, and we would be discarding important information if we exclude them from a final analysis.
There is a negative slope in the line shown in Figure \(\PageIndex{1}\). However, this slope (and the y-intercept) are only estimates of the parameter values. We might wonder, is this convincing evidence that the "true" linear model has a negative slope? That is, do the data provide strong evidence that the political theory is accurate? We can frame this investigation into a one-sided statistical hypothesis test:
- H 0 : \(\beta _1 = 0\). The true linear model has slope zero.
- HA: \(\beta _1 < 0\). The true linear model has a slope less than zero. The higher the unemployment, the greater the losses for the President's party in the House of Representatives.
We would reject H 0 in favor of H A if the data provide strong evidence that the true slope parameter is less than zero. To assess the hypotheses, we identify a standard error for the estimate, compute an appropriate test statistic, and identify the p-value.
Understanding regression output from software
Just like other point estimates we have seen before, we can compute a standard error and test statistic for \(\beta_1\). We will generally label the test statistic using a T, since it follows the t distribution.
We will rely on statistical software to compute the standard error and leave the explanation of how this standard error is determined to a second or third statistics course. Table \(\PageIndex{1}\) shows software output for the least squares regression line in Figure \(\PageIndex{1}\). The row labeled unemp represents the information for the slope, which is the coefficient of the unemployment variable.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | -6.7142 |
5.4567 |
-1.23 |
0.2300 |
| unemp | -1.0010 | 0.8717 | -1.15 | 0.2617 |
Example \(\PageIndex{2}\)
What do the first and second columns of Table \(\PageIndex{1}\) represent?
Solution
The entries in the first column represent the least squares estimates, \(\beta_0\) and \(\beta_1\), and the values in the second column correspond to the standard errors of each estimate.
We previously used a t test statistic for hypothesis testing in the context of numerical data. Regression is very similar. In the hypotheses we consider, the null value for the slope is 0, so we can compute the test statistic using the T (or Z) score formula:
\[T = \frac {\text {estimate - null value}}{SE} = \frac {-1.0010 - 0}{0.8717} = -1.15 \nonumber\]
We can look for the one-sided p-value - shown in Figure \(\PageIndex{2}\) - using the probability table for the t distribution in Appendix B.2
Exercise \(\PageIndex{2}\)
Table \(\PageIndex{1}\) offers the degrees of freedom for the test statistic T: df = 25. Identify the p-value for the hypothesis test.
- Answer
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Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.
Looking in the 25 degrees of freedom row in Appendix B.2, we see that the absolute value of the test statistic is smaller than any value listed, which means the tail area and therefore also the p-value is larger than 0.100 (one tail!). Because the p-value is so large, we fail to reject the null hypothesis. That is, the data do not provide convincing evidence that a higher unemployment rate has any correspondence with smaller or larger losses for the President's party in the House of Representatives in midterm elections.
We could have identified the t test statistic from the software output in Table \(\PageIndex{1}\), shown in the second row (unemp) and third column (t value). The entry in the second row and last column in Table \(\PageIndex{1}\) represents the p-value for the two-sided hypothesis test where the null value is zero. The corresponding one-sided test would have a p-value half of the listed value.
Inference for regression
We usually rely on statistical software to identify point estimates and standard errors for parameters of a regression line. After verifying conditions hold for fitting a line, we can use the methods learned in Section 5.3 for the t distribution to create con dence intervals for regression parameters or to evaluate hypothesis tests.
Caution: Don't carelessly use the p-value from regression output
The last column in regression output often lists p-values for one particular hypothesis: a two-sided test where the null value is zero. If your test is one-sided and the point estimate is in the direction of HA, then you can halve the software's p-value to get the one-tail area. If neither of these scenarios match your hypothesis test, be cautious about using the software output to obtain the p-value.
Example \(\PageIndex{3}\)
Examine Figure 7.16, which relates the Elmhurst College aid and student family income. How sure are you that the slope is statistically significantly different from zero? That is, do you think a formal hypothesis test would reject the claim that the true slope of the line should be zero?
Solution
While the relationship between the variables is not perfect, there is an evident decreasing trend in the data. This suggests the hypothesis test will reject the null claim that the slope is zero.
Exercise \(\PageIndex{3}\)
Table \(\PageIndex{2}\) shows statistical software output from tting the least squares regression line shown in Figure 7.16. Use this output to formally evaluate the following hypotheses.
- H 0 : The true coefficient for family income is zero.
- H A : The true coefficient for family income is not zero.
| Estimate | Std. Error | t value |
Pr(>|t|) |
|
|---|---|---|---|---|
|
(Intercept) family_income |
24.3193 -0.0431 |
1.2915 0.0108 |
18.83 -3.98 |
0.0000 0.0002 |
- Answer
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We look in the second row corresponding to the family income variable. We see the point estimate of the slope of the line is -0.0431, the standard error of this estimate is 0.0108, and the t test statistic is -3.98. The p-value corresponds exactly to the two-sided test we are interested in: 0.0002. The p-value is so small that we reject the null hypothesis and conclude that family income and nancial aid at Elmhurst College for freshman entering in the year 2011 are negatively correlated and the true slope parameter is indeed less than 0, just as we believed in Example 7.27.
TIP: Always check assumptions
If conditions for tting the regression line do not hold, then the methods presented here should not be applied. The standard error or distribution assumption of the point estimate - assumed to be normal when applying the t test statistic - may not be valid.
An alternative Test Statistic
We considered the t test statistic as a way to evaluate the strength of evidence for a hypothesis test in Section 7.4.2. However, we could focus on R 2 . Recall that R 2 described the proportion of variability in the response variable (y) explained by the explanatory variable (x). If this proportion is large, then this suggests a linear relationship exists between the variables. If this proportion is small, then the evidence provided by the data may not be convincing.
This concept - considering the amount of variability in the response variable explained by the explanatory variable - is a key component in some statistical techniques. The analysis of variance (ANOVA) technique introduced in Section 5.5 uses this general principle. The method states that if enough variability is explained away by the categories, then we would conclude the mean varied between the categories. On the other hand, we might not be convinced if only a little variability is explained. ANOVA can be further employed in advanced regression modeling to evaluate the inclusion of explanatory variables, though we leave these details to a later course.


7.1: Vitamins: Basic Concepts
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Skills to Develop
- Define vitamin
- Know the difference between fat soluble and water soluble vitamins
- Recognize the names of each of the 13 vitamins
- For each vitamin, know what the vitamin does and what happens to the human body if: the vitamin is too low in the diet for too long (deficiency); the vitamin is too high in the diet for too long (toxicity) and be able to list some food sources that are rich in each of the vitamins.
Vitamins are organic compounds (meaning they contain Carbon) and they are vital nutrients that organisms require in limited amounts. Just like other essential nutrients, vitamins must be obtained from the diet since the organism can not make them (or can not make enough of them) for survival. Interestingly, not all organisms have the same vitamin requirements. For example, ascorbic acid (one form of vitamin C) is a vitamin for humans, because the human body can not make it for us, but most all other animals have the ability to make this vitamin for themselves.
Thirteen vitamins are universally recognized. Some researchers believe there are more vitamins that have yet to be discovered. Vitamins are classified as either: fat soluble (will dissolve in oil) or water soluble (will dissolve in water). Only four of the vitamins: A, D, E and K are fat soluble. The other 9 vitamins are water soluble, including: vitamin C and all of the B vitamins (Riboflavin, Niacin, Thiamin, B 6 , Folate, B 12 , Pantothenic Acid and Biotin). It is also important to note that, the term "vitamin" can refer to a number of compounds that all show the biological activity associated with a particular vitamin. For example, "vitamin A", includes the compounds: retinal, retinol, retinoic acid and four known carotenoids. All of these compounds can be converted into active vitamin A in the body and are therefore considered to be precursors to vitamin A.
Vitamins have diverse biochemical functions. Most of the vitamins have several important functions, not just one. Some vitamins, such as vitamin D and A, have hormone-like functions where they travel through the blood and tell certain cell types what to do. Other vitamins function as antioxidants (vitamin E and vitamin C for example). The largest number of vitamins, the B complex vitamins, function primarily as "enzyme helpers" called coenzymes . Coenzymes are needed for enzymes to function.
Vitamins are needed in very small quantities. When you look at Table \(\PageIndex{1}\), at the amounts needed, you'll see that the vitamins are measured in microgram (µg) or milligram (mg) amounts. Remember that there are 1,000 mg in 1 gram and 1,000 micrograms in 1 milligram.  As you read about each of the vitamins and their important roles in human health, keep in mind there can be too much of a good thing. These days, people sometimes choose to take large doses of vitamin supplements. Large doses of vitamin supplements can make it easy to get to toxic amounts of vitamins. I encourage you to think of vitamins as being on a continuum where you can be deficient (too low), just right, or toxic (too high). If you are just a little deficient you may only be able to detect the deficiency with a blood test but if you are deficient long enough and severe enough, systems of the body will eventually begin to lose function and you will see signs and symptoms overtly. At that stage it is called a "deficiency disease". If a deficiency disease is caught early enough it can usually be reversed by giving the person the vitamin they were deficient in but in some cases the damage that has been done is too severe and can not be reversed.
Exercise
Please click on the vitamin name below and you will be linked to a Wikipedia article to learn about that vitamin. Keep in mind, for quiz/exam purposes, you're looking for: function (what does the vitamin do?), deficiency symptoms (what happens if I'm too low for too long), toxicity symptoms (what happens if I have too much for too long?) and food sources (what can I eat to get more of this vitamin) for each of the 13 vitamins.
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Vitamin generic
descriptor name |
Vitamin chemical name(s) |
Solubility
(fat or water) |
Recommended dietary allowances
(male, age 19–70) |
Deficiency disease |
Upper Intake Level
(UL/day) |
Overdose disease | Food sources |
|---|---|---|---|---|---|---|---|
| Vitamin A |
Retinol, retinal, and
four carotenoids including beta carotene |
Fat | 900 µg | Night blindness, hyperkeratosis, and keratomalacia | 3,000 µg | Hypervitaminosis A | Liver, orange, ripe yellow fruits, leafy vegetables, carrots, pumpkin, squash, spinach, fish, soya milk, milk |
| Vitamin B 1 | Thiamine | Water | 1.2 mg | Beriberi, Wernicke-Korsakoff syndrome | N/D [10] | Drowsiness or muscle relaxation with large doses. | Pork, oatmeal, brown rice, vegetables, potatoes, liver, eggs |
| Vitamin B 2 | Riboflavin | Water | 1.3 mg | Ariboflavinosis, glossitis, angular stomatitis | N/D | Dairy products, bananas, popcorn, green beans, asparagus | |
| Vitamin B 3 | Niacin, niacinamide | Water | 16.0 mg | Pellagra | 35.0 mg | Liver damage (doses > 2g/day) and other problems | Meat, fish, eggs, many vegetables, mushrooms, tree nuts |
| Vitamin B 5 | Pantothenic acid | Water | 5.0 mg [13] | Paresthesia | N/D | Diarrhea; possibly nausea and heartburn. | Meat, broccoli, avocados |
| Vitamin B 6 | Pyridoxine, pyridoxamine, pyridoxal | Water | 1.3–1.7 mg | Anemia [15] peripheral neuropathy | 100 mg | Impairment of proprioception, nerve damage (doses > 100 mg/day) | Meat, vegetables, tree nuts, bananas |
| Vitamin B 7 | Biotin | Water | 30.0 µg | Dermatitis, enteritis | N/D | Raw egg yolk, liver, peanuts, leafy green vegetables | |
| Vitamin B 9 | Folic acid, folate, folinic acid | Water | 400 µg | Megaloblastic anemia and deficiency during pregnancy is associated with birth defects, such as neural tube defects | 1,000 µg | May mask symptoms of vitamin B 12 deficiency; other effects. | Leafy vegetables, pasta, bread, cereal, liver |
| Vitamin B 12 | Cyanocobalamin, hydroxocobalamin, methylcobalamin | Water | 2.4 µg | Megaloblastic anemia [16] | N/D | Acne-like rash [causality is not conclusively established]. | Meat and other animal products |
| Vitamin C | Ascorbic acid | Water | 90.0 mg | Scurvy | 2,000 mg | Vitamin C megadosage | Many fruits and vegetables, liver |
| Vitamin D | Cholecalciferol (D3), Ergocalciferol (D2) | Fat | 10 µg [17] | Rickets and osteomalacia | 50 µg | Hypervitaminosis D | Fish, eggs, liver, mushrooms |
| Vitamin E | Tocopherols, tocotrienols | Fat | 15.0 mg | Deficiency is very rare; sterility in males and abortions in females, mild hemolytic anemia in newborn infants [18] | 1,000 mg | Increased congestive heart failure seen in one large randomized study. | Many fruits and vegetables, nuts and seeds |
| Vitamin K | phylloquinone, menaquinones | Fat | 120 µg | Bleeding diathesis | N/D | Increases coagulation in patients taking warfarin. | Leafy green vegetables such as spinach, egg yolks, |
Health Effects
Vitamins are essential for the normal growth and development of a multicellular organism. Using the genetic blueprint inherited from its parents, a fetus begins to develop, at the moment of conception, from the nutrients it absorbs. It requires certain vitamins and minerals to be present at certain times. These nutrients facilitate the chemical reactions that produce among other things, skin, bone, and muscle. If there is serious deficiency in one or more of these nutrients, a child may develop a deficiency disease. Even minor deficiencies may cause permanent damage.[21]
For the most part, vitamins are obtained with food, but a few are obtained by other means. For example, microorganisms in the intestine — commonly known as "gut flora" — produce vitamin K and biotin, while one form of vitamin D is synthesized in the skin with the help of the natural ultraviolet wavelength of sunlight. Humans can produce some vitamins from precursors they consume. Examples include vitamin A, produced from beta carotene, and niacin, from the amino acid tryptophan.
Once growth and development are completed, vitamins remain essential nutrients for the healthy maintenance of the cells, tissues, and organs that make up a multicellular organism; they also enable a multicellular life form to efficiently use chemical energy provided by food it eats, and to help process the proteins, carbohydrates, and fats required for respiration.
Deficiencies
Humans must consume vitamins periodically but with differing schedules, to avoid deficiency. The human body's stores for different vitamins vary widely; vitamins A, D, and B 12 are stored in significant amounts in the human body, mainly in the liver, and an adult human's diet may be deficient in vitamins A and D for many months and B 12 in some cases for years, before developing a deficiency condition. However, vitamin B 3 (niacin and niacinamide) is not stored in the human body in significant amounts, so stores may last only a couple of weeks. For vitamin C, the first symptoms of scurvy in experimental studies of complete vitamin C deprivation in humans have varied widely, from a month to more than six months, depending on previous dietary history that determined body stores.
Deficiencies of vitamins are classified as either primary or secondary. A primary deficiency occurs when an organism does not get enough of the vitamin in its food. A secondary deficiency may be due to an underlying disorder that prevents or limits the absorption or use of the vitamin, due to a "lifestyle factor", such as smoking, excessive alcohol consumption, or the use of medications that interfere with the absorption or use of the vitamin. People who eat a varied diet are unlikely to develop a severe primary vitamin deficiency. In contrast, restrictive diets have the potential to cause prolonged vitamin deficits, which may result in often painful and potentially deadly diseases.
Well-known human vitamin deficiencies involve thiamine (beriberi), niacin (pellagra), vitamin C (scurvy), and vitamin D (rickets). In much of the developed world, such deficiencies are rare; this is due to (1) an adequate supply of food and (2) the addition of vitamins and minerals to common foods, often called fortification. In addition to these classical vitamin deficiency diseases, some evidence has also suggested links between vitamin deficiency and a number of different disorders.
Side-effects
In large doses, some vitamins have documented side-effects that tend to be more severe with a larger dosage. The likelihood of consuming too much of any vitamin from food is remote, but overdosing (vitamin poisoning) from vitamin supplementation does occur. At high enough dosages, some vitamins cause side-effects such as nausea, diarrhea, and vomiting. When side-effects emerge, recovery is often accomplished by reducing the dosage. The doses of vitamins differ because individual tolerances can vary widely and appear to be related to age and state of health. In 2008, overdose exposure to all formulations of vitamins and multivitamin-mineral formulations was reported by 68,911 individuals to the American Association of Poison Control Centers (nearly 80% of these exposures were in children under the age of 6), leading to 8 "major" life-threatening outcomes, but no deaths.
Governmental regulation
Most countries place dietary supplements in a special category under the general umbrella of foods, not drugs. As a result, the manufacturer, and not the government, has the responsibility of ensuring that its dietary supplement products are safe before they are marketed. Regulation of supplements varies widely by country. In the United States, a dietary supplement is defined under the Dietary Supplement Health and Education Act of 1994.[55] There is no FDA approval process for dietary supplements, and no requirement that manufacturers prove the safety or efficacy of supplements introduced before 1994.[32][33] The Food and Drug Administration must rely on its Adverse Event Reporting System to monitor adverse events that occur with supplements.[56] In 2007, the US Code of Federal Regulations (CFR) Title 21, part III took effect, regulating GMP practices in the manufacturing, packaging, labeling, or holding operations for dietary supplements. Even though product registration is not required, these regulations mandate production and quality control standards (including testing for identity, purity and adulterations) for dietary supplements.[57] In the European Union, the Food Supplements Directive requires that only those supplements that have been proven safe can be sold without a prescription.[58] For most vitamins, pharmacopoeial standards have been established. In the United States, the United States Pharmacopeia (USP) sets standards for the most commonly used vitamins and preparations thereof. Likewise, monographs of the European Pharmacopoeia (Ph.Eur.) regulate aspects of identity and purity for vitamins on the European market.
Contributors and Attributions
- Wikipedia. The content on this page is licensesed under a CC-BY-SA 4.0 licences in contract to that for the rest of the medicine library.