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College Physics for AP® Courses 2e | Circuits and DC Instruments | Null Measurements | m42362 | Resistance Measurements and the Wheatstone Bridge | There is a variety of so-called ohmmeters that purport to measure resistance. What the most common ohmmeters actually do is to apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm’s law. Their readout is this calculated resistance. Two configurations for ohmmeters using standard voltmeters and ammeters are shown in [link]. Such configurations are limited in accuracy, because the meters alter both the voltage applied to the resistor and the current that flows through it. |
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College Physics for AP® Courses 2e | Circuits and DC Instruments | DC Circuits Containing Resistors and Capacitors | * Explain the importance of the time constant, τ , and calculate the time constant for a given resistance and capacitance.
* Explain why batteries in a flashlight gradually lose power and the light dims over time.
* Describe what happens to a graph of the voltage across a capacitor over time as it charges.
* Explain how a timing circuit works and list some applications.
* Calculate the necessary speed of a strobe flash needed to “stop” the movement of an object over a particular length. | m42363 | *RC* Circuits | An *RC* circuit is one containing a resistor *R* and a capacitor *C*. The capacitor is an electrical component that stores electric charge. |
College Physics for AP® Courses 2e | Circuits and DC Instruments | DC Circuits Containing Resistors and Capacitors | * Explain the importance of the time constant, τ , and calculate the time constant for a given resistance and capacitance.
* Explain why batteries in a flashlight gradually lose power and the light dims over time.
* Describe what happens to a graph of the voltage across a capacitor over time as it charges.
* Explain how a timing circuit works and list some applications.
* Calculate the necessary speed of a strobe flash needed to “stop” the movement of an object over a particular length. | m42363 | Discharging a Capacitor | Discharging a capacitor through a resistor proceeds in a similar fashion, as [link] illustrates. Initially, the current is ${I}_{0}=\frac{{V}_{0}}{R}$, driven by the initial voltage ${V}_{0}$ on the capacitor. As the voltage decreases, the current and hence the rate of discharge decreases, implying another exponential formula for $V$. Using calculus, the voltage $V$ on a capacitor $C$ being discharged through a resistor $R$ is found to be |
College Physics for AP® Courses 2e | Circuits and DC Instruments | DC Circuits Containing Resistors and Capacitors | * Explain the importance of the time constant, τ , and calculate the time constant for a given resistance and capacitance.
* Explain why batteries in a flashlight gradually lose power and the light dims over time.
* Describe what happens to a graph of the voltage across a capacitor over time as it charges.
* Explain how a timing circuit works and list some applications.
* Calculate the necessary speed of a strobe flash needed to “stop” the movement of an object over a particular length. | m42363 | *RC* Circuits for Timing | $\text{RC}$ circuits are commonly used for timing purposes. A mundane example of this is found in the ubiquitous intermittent wiper systems of modern cars. The time between wipes is varied by adjusting the resistance in an $\text{RC}$ circuit. Another example of an $\text{RC}$ circuit is found in novelty jewelry, Halloween costumes, and various toys that have battery-powered flashing lights. (See [link] for a timing circuit.) |
College Physics for AP® Courses 2e | Magnetism | Connection for AP® Courses | m55372 | |||
College Physics for AP® Courses 2e | Magnetism | Magnets | m42366 | |||
College Physics for AP® Courses 2e | Magnetism | Ferromagnets and Electromagnets | m42368 | Ferromagnets | Only certain materials, such as iron, cobalt, nickel, and gadolinium, exhibit strong magnetic effects. Such materials are called ferromagnetic, after the Latin word for iron, *ferrum*. A group of materials made from the alloys of the rare earth elements are also used as strong and permanent magnets; a popular one is neodymium. Other materials exhibit weak magnetic effects, which are detectable only with sensitive instruments. Not only do ferromagnetic materials respond strongly to magnets (the way iron is attracted to magnets), they can also be magnetized themselves—that is, they can be induced to be magnetic or made into permanent magnets. |
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College Physics for AP® Courses 2e | Magnetism | Ferromagnets and Electromagnets | m42368 | Electromagnets | Early in the 19th century, it was discovered that electrical currents cause magnetic effects. The first significant observation was by the Danish scientist Hans Christian Oersted (1777–1851), who found that a compass needle was deflected by a current-carrying wire. This was the first significant evidence that the movement of charges had any connection with magnets. Electromagnetism is the use of electric current to make magnets. These temporarily induced magnets are called electromagnets. Electromagnets are employed for everything from a wrecking yard crane that lifts scrapped cars to controlling the beam of a 90-km-circumference particle accelerator to the magnets in medical imaging machines (See [link]). |
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College Physics for AP® Courses 2e | Magnetism | Ferromagnets and Electromagnets | m42368 | Current: The Source of All Magnetism | An electromagnet creates magnetism with an electric current. In later sections we explore this more quantitatively, finding the strength and direction of magnetic fields created by various currents. But what about ferromagnets? [link] shows models of how electric currents create magnetism at the submicroscopic level. (Note that we cannot directly observe the paths of individual electrons about atoms, and so a model or visual image, consistent with all direct observations, is made. We can directly observe the electron’s orbital angular momentum, its spin momentum, and subsequent magnetic moments, all of which are explained with electric-current-creating subatomic magnetism.) Currents, including those associated with other submicroscopic particles like protons, allow us to explain ferromagnetism and all other magnetic effects. Ferromagnetism, for example, results from an internal cooperative alignment of electron spins, possible in some materials but not in others. |
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College Physics for AP® Courses 2e | Magnetism | Magnetic Fields and Magnetic Field Lines | m42370 | |||
College Physics for AP® Courses 2e | Magnetism | Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field | m42372 | Right Hand Rule 1 | The magnetic force on a moving charge is one of the most fundamental known. Magnetic force is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex, in both the number of factors that affects it and in its direction, than the relatively simple Coulomb force. The magnitude of the magnetic force $F$ on a charge $q$ moving at a speed $v$ in a magnetic field of strength $B$ is given by |
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College Physics for AP® Courses 2e | Magnetism | Force on a Moving Charge in a Magnetic Field: Examples and Applications | m42375 | |||
College Physics for AP® Courses 2e | Magnetism | The Hall Effect | m42377 | |||
College Physics for AP® Courses 2e | Magnetism | Magnetic Force on a Current-Carrying Conductor | m42398 | |||
College Physics for AP® Courses 2e | Magnetism | Torque on a Current Loop: Motors and Meters | m42380 | |||
College Physics for AP® Courses 2e | Magnetism | Magnetic Fields Produced by Currents: Ampere’s Law | m42382 | Magnetic Field Created by a Long Straight Current-Carrying Wire: Right Hand Rule 2 | Magnetic fields have both direction and magnitude. As noted before, one way to explore the direction of a magnetic field is with compasses, as shown for a long straight current-carrying wire in [link]. Hall probes can determine the magnitude of the field. The field around a long straight wire is found to be in circular loops. The right hand rule 2 (RHR-2) emerges from this exploration and is valid for any current segment—*point the thumb in the direction of the current, and the fingers curl in the direction of the magnetic field loops* created by it. |
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College Physics for AP® Courses 2e | Magnetism | Magnetic Fields Produced by Currents: Ampere’s Law | m42382 | Ampere’s Law and Others | The magnetic field of a long straight wire has more implications than you might at first suspect. *Each segment of current produces a magnetic field like that of a long straight wire, and the total field of any shape current is the vector sum of the fields due to each segment.* The formal statement of the direction and magnitude of the field due to each segment is called the Biot-Savart law. Integral calculus is needed to sum the field for an arbitrary shape current. This results in a more complete law, called Ampere’s law, which relates magnetic field and current in a general way. Ampere’s law in turn is a part of Maxwell’s equations, which give a complete theory of all electromagnetic phenomena. Considerations of how Maxwell’s equations appear to different observers led to the modern theory of relativity, and the realization that electric and magnetic fields are different manifestations of the same thing. Most of this is beyond the scope of this text in both mathematical level, requiring calculus, and in the amount of space that can be devoted to it. But for the interested student, and particularly for those who continue in physics, engineering, or similar pursuits, delving into these matters further will reveal descriptions of nature that are elegant as well as profound. In this text, we shall keep the general features in mind, such as RHR-2 and the rules for magnetic field lines listed in Magnetic Fields and Magnetic Field Lines, while concentrating on the fields created in certain important situations. |
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College Physics for AP® Courses 2e | Magnetism | Magnetic Fields Produced by Currents: Ampere’s Law | m42382 | Magnetic Field Produced by a Current-Carrying Circular Loop | The magnetic field near a current-carrying loop of wire is shown in [link]. Both the direction and the magnitude of the magnetic field produced by a current-carrying loop are complex. RHR-2 can be used to give the direction of the field near the loop, but mapping with compasses and the rules about field lines given in Magnetic Fields and Magnetic Field Lines are needed for more detail. There is a simple formula for the magnetic field strength at the center of a circular loop. It is |
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College Physics for AP® Courses 2e | Magnetism | Magnetic Fields Produced by Currents: Ampere’s Law | m42382 | Magnetic Field Produced by a Current-Carrying Solenoid | A solenoid is a long coil of wire (with many turns or loops, as opposed to a flat loop). Because of its shape, the field inside a solenoid can be very uniform, and also very strong. The field just outside the coils is nearly zero. [link] shows how the field looks and how its direction is given by RHR-2. |
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College Physics for AP® Courses 2e | Magnetism | Magnetic Force between Two Parallel Conductors | m42386 | |||
College Physics for AP® Courses 2e | Magnetism | More Applications of Magnetism | m42388 | Mass Spectrometry | The curved paths followed by charged particles in magnetic fields can be put to use. A charged particle moving perpendicular to a magnetic field travels in a circular path having a radius $r$. |
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College Physics for AP® Courses 2e | Magnetism | More Applications of Magnetism | m42388 | Cathode Ray Tubes—CRTs—and the Like | What do non-flat-screen TVs, old computer monitors, x-ray machines, and the 2-mile-long Stanford Linear Accelerator have in common? All of them accelerate electrons, making them different versions of the electron gun. Many of these devices use magnetic fields to steer the accelerated electrons. [link] shows the construction of the type of cathode ray tube (CRT) found in some TVs, oscilloscopes, and old computer monitors. Two pairs of coils are used to steer the electrons, one vertically and the other horizontally, to their desired destination. |
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College Physics for AP® Courses 2e | Magnetism | More Applications of Magnetism | m42388 | Magnetic Resonance Imaging | Magnetic resonance imaging (MRI) is one of the most useful and rapidly growing medical imaging tools. It non-invasively produces two-dimensional and three-dimensional images of the body that provide important medical information with none of the hazards of x-rays. MRI is based on an effect called nuclear magnetic resonance (NMR) in which an externally applied magnetic field interacts with the nuclei of certain atoms, particularly those of hydrogen (protons). These nuclei possess their own small magnetic fields, similar to those of electrons and the current loops discussed earlier in this chapter. |
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College Physics for AP® Courses 2e | Magnetism | More Applications of Magnetism | m42388 | Other Medical Uses of Magnetic Fields | Currents in nerve cells and the heart create magnetic fields like any other currents. These can be measured but with some difficulty since their strengths are about ${\text{10}}^{-6}$ to ${\text{10}}^{-8}$ *less* than the Earth’s magnetic field. Recording of the heart’s magnetic field as it beats is called a magnetocardiogram (MCG), while measurements of the brain’s magnetic field is called a magnetoencephalogram (MEG). Both give information that differs from that obtained by measuring the electric fields of these organs (ECGs and EEGs), but they are not yet of sufficient importance to make these difficult measurements common. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Connection for AP® Courses | m55405 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Induced Emf and Magnetic Flux | m42390 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Faraday’s Law of Induction: Lenz’s Law | m42392 | Faraday’s and Lenz’s Law | Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to the change in flux $\Delta \Phi$. Second, emf is greatest when the change in time $\Delta t$ is smallest—that is, emf is inversely proportional to $\Delta t$. Finally, if a coil has $N$ turns, an emf will be produced that is $N$ times greater than for a single coil, so that emf is directly proportional to $N$. The equation for the emf induced by a change in magnetic flux is |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Faraday’s Law of Induction: Lenz’s Law | m42392 | Applications of Electromagnetic Induction | There are many applications of Faraday’s Law of induction, as we will explore in this chapter and others. At this juncture, let us mention several that have to do with data storage and magnetic fields. A very important application has to do with audio and video *recording tapes*. A plastic tape, coated with iron oxide, moves past a recording head. This recording head is basically a round iron ring about which is wrapped a coil of wire—an electromagnet ([link]). A signal in the form of a varying input current from a microphone or camera goes to the recording head. These signals (which are a function of the signal amplitude and frequency) produce varying magnetic fields at the recording head. As the tape moves past the recording head, the magnetic field orientations of the iron oxide molecules on the tape are changed thus recording the signal. In the playback mode, the magnetized tape is run past another head, similar in structure to the recording head. The different magnetic field orientations of the iron oxide molecules on the tape induces an emf in the coil of wire in the playback head. This signal then is sent to a loudspeaker or video player. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Motional Emf | m42400 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Eddy Currents and Magnetic Damping | m42404 | Eddy Currents and Magnetic Damping | As discussed in Motional Emf, motional emf is induced when a conductor moves in a magnetic field or when a magnetic field moves relative to a conductor. If motional emf can cause a current loop in the conductor, we refer to that current as an eddy current. Eddy currents can produce significant drag, called magnetic damping, on the motion involved. Consider the apparatus shown in [link], which swings a pendulum bob between the poles of a strong magnet. (This is another favorite physics lab activity.) If the bob is metal, there is significant drag on the bob as it enters and leaves the field, quickly damping the motion. If, however, the bob is a slotted metal plate, as shown in [link](b), there is a much smaller effect due to the magnet. There is no discernible effect on a bob made of an insulator. Why is there drag in both directions, and are there any uses for magnetic drag? |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Eddy Currents and Magnetic Damping | m42404 | Applications of Magnetic Damping | One use of magnetic damping is found in sensitive laboratory balances. To have maximum sensitivity and accuracy, the balance must be as friction-free as possible. But if it is friction-free, then it will oscillate for a very long time. Magnetic damping is a simple and ideal solution. With magnetic damping, drag is proportional to speed and becomes zero at zero velocity. Thus the oscillations are quickly damped, after which the damping force disappears, allowing the balance to be very sensitive. (See [link].) In most balances, magnetic damping is accomplished with a conducting disc that rotates in a fixed field. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Electric Generators | m42408 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Back Emf | m42411 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Transformers | m42414 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Electrical Safety: Systems and Devices | m42416 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Inductance | m42420 | Inductors | Induction is the process in which an emf is induced by changing magnetic flux. Many examples have been discussed so far, some more effective than others. Transformers, for example, are designed to be particularly effective at inducing a desired voltage and current with very little loss of energy to other forms. Is there a useful physical quantity related to how “effective” a given device is? The answer is yes, and that physical quantity is called inductance. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Inductance | m42420 | Energy Stored in an Inductor | We know from Lenz’s law that inductances oppose changes in current. There is an alternative way to look at this opposition that is based on energy. Energy is stored in a magnetic field. It takes time to build up energy, and it also takes time to deplete energy; hence, there is an opposition to rapid change. In an inductor, the magnetic field is directly proportional to current and to the inductance of the device. It can be shown that the energy stored in an inductor ${E}_{\text{ind}}$ is given by |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | RL Circuits | m42425 | |||
College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Reactance, Inductive and Capacitive | m42427 | Inductors and Inductive Reactance | Suppose an inductor is connected directly to an AC voltage source, as shown in [link]. It is reasonable to assume negligible resistance, since in practice we can make the resistance of an inductor so small that it has a negligible effect on the circuit. Also shown is a graph of voltage and current as functions of time. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Reactance, Inductive and Capacitive | m42427 | Capacitors and Capacitive Reactance | Consider the capacitor connected directly to an AC voltage source as shown in [link]. The resistance of a circuit like this can be made so small that it has a negligible effect compared with the capacitor, and so we can assume negligible resistance. Voltage across the capacitor and current are graphed as functions of time in the figure. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | Reactance, Inductive and Capacitive | m42427 | Resistors in an AC Circuit | Just as a reminder, consider [link], which shows an AC voltage applied to a resistor and a graph of voltage and current versus time. The voltage and current are exactly *in* *phase* in a resistor. There is no frequency dependence to the behavior of plain resistance in a circuit: |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | RLC Series AC Circuits | m42431 | Impedance | When alone in an AC circuit, inductors, capacitors, and resistors all impede current. How do they behave when all three occur together? Interestingly, their individual resistances in ohms do not simply add. Because inductors and capacitors behave in opposite ways, they partially to totally cancel each other’s effect. [link] shows an *RLC* series circuit with an AC voltage source, the behavior of which is the subject of this section. The crux of the analysis of an *RLC* circuit is the frequency dependence of ${X}_{L}$ and ${X}_{C}$, and the effect they have on the phase of voltage versus current (established in the preceding section). These give rise to the frequency dependence of the circuit, with important “resonance” features that are the basis of many applications, such as radio tuners. |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | RLC Series AC Circuits | m42431 | Resonance in *RLC* Series AC Circuits | How does an *RLC* circuit behave as a function of the frequency of the driving voltage source? Combining Ohm’s law, ${I}_{\text{rms}}={V}_{\text{rms}}/Z$, and the expression for impedance $Z$ from $Z=\sqrt{{R}^{2}+\left({X}_{L}-{X}_{C}{\right)}^{2}}$ gives |
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College Physics for AP® Courses 2e | Electromagnetic Induction, AC Circuits, and Electrical Technologies | RLC Series AC Circuits | m42431 | Power in *RLC* Series AC Circuits | If current varies with frequency in an *RLC* circuit, then the power delivered to it also varies with frequency. But the average power is not simply current times voltage, as it is in purely resistive circuits. As was seen in [link], voltage and current are out of phase in an *RLC* circuit. There is a phase angle $\varphi$ between the source voltage $V$ and the current $I$, which can be found from |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Connection for AP® Courses | m55423 | Discovering a New Phenomenon | It is worth noting at the outset that the general phenomenon of electromagnetic waves was predicted by theory before it was realized that light is a form of electromagnetic wave. The prediction was made by James Clerk Maxwell in the mid-19th century when he formulated a single theory combining all the electric and magnetic effects known by scientists at that time. “Electromagnetic waves” was the name he gave to the phenomena his theory predicted. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Maxwell’s Equations: Electromagnetic Waves Predicted and Observed | m42437 | Hertz’s Observations | The German physicist Heinrich Hertz (1857–1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. Starting in 1887, he performed a series of experiments that not only confirmed the existence of electromagnetic waves, but also verified that they travel at the speed of light. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Production of Electromagnetic Waves | m42440 | Electric and Magnetic Waves: Moving Together | Following Ampere’s law, current in the antenna produces a magnetic field, as shown in [link]. The relationship between $\mathbf{E}$ and $\mathbf{B}$ is shown at one instant in [link] (a). As the current varies, the magnetic field varies in magnitude and direction. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Production of Electromagnetic Waves | m42440 | Receiving Electromagnetic Waves | Electromagnetic waves carry energy away from their source, similar to a sound wave carrying energy away from a standing wave on a guitar string. An antenna for receiving EM signals works in reverse. And like antennas that produce EM waves, receiver antennas are specially designed to resonate at particular frequencies. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Production of Electromagnetic Waves | m42440 | Relating $E$-Field and $B$-Field Strengths | There is a relationship between the $E$- and $B$-field strengths in an electromagnetic wave. This can be understood by again considering the antenna just described. The stronger the $E$-field created by a separation of charge, the greater the current and, hence, the greater the $B$-field created. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Transmission, Reflection, and Absorption | What happens when an electromagnetic wave impinges on a material? If the material is transparent to the particular frequency, then the wave can largely be transmitted. If the material is opaque to the frequency, then the wave can be totally reflected. The wave can also be absorbed by the material, indicating that there is some interaction between the wave and the material, such as the thermal agitation of molecules. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Radio and TV Waves | The broad category of radio waves is defined to contain any electromagnetic wave produced by currents in wires and circuits. Its name derives from their most common use as a carrier of audio information (i.e., radio). The name is applied to electromagnetic waves of similar frequencies regardless of source. Radio waves from outer space, for example, do not come from alien radio stations. They are created by many astronomical phenomena, and their study has revealed much about nature on the largest scales. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | FM Radio Waves | FM radio waves are also used for commercial radio transmission, but in the frequency range of 88 to 108 MHz. FM stands for frequency modulation, another method of carrying information. (See [link].) Here a carrier wave having the basic frequency of the radio station, perhaps 105.1 MHz, is modulated in frequency by the audio signal, producing a wave of constant amplitude but varying frequency. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Radio Wave Interference | Astronomers and astrophysicists collect signals from outer space using electromagnetic waves. A common problem for astrophysicists is the “pollution” from electromagnetic radiation pervading our surroundings from communication systems in general. Even everyday gadgets like our car keyless entry devices and remote starters and being able to turn TVs on and off using remotes involve radio-wave frequencies. In order to prevent interference between all these electromagnetic signals, strict regulations are drawn up for different organizations to utilize different radio frequency bands. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Microwaves | Microwaves are the highest-frequency electromagnetic waves that can be produced by currents in macroscopic circuits and devices. Microwave frequencies range from about ${\text{10}}^{9}{\rule{0.25em}{0ex}}\text{Hz}$ to the highest practical $\text{LC}$ resonance at nearly ${\text{10}}^{\text{12}}{\rule{0.25em}{0ex}}\text{Hz}$. Since they have high frequencies, their wavelengths are short compared with those of other radio waves—hence the name “microwave.” |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Heating with Microwaves | How does the ubiquitous microwave oven produce microwaves electronically, and why does food absorb them preferentially? Microwaves at a frequency of 2.45 GHz are produced by accelerating electrons. The microwaves are then used to induce an alternating electric field in the oven. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Infrared Radiation | The microwave and infrared regions of the electromagnetic spectrum overlap (see [link]). Infrared radiation is generally produced by thermal motion and the vibration and rotation of atoms and molecules. Electronic transitions in atoms and molecules can also produce infrared radiation. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Visible Light | Visible light is the narrow segment of the electromagnetic spectrum to which the normal human eye responds. Visible light is produced by vibrations and rotations of atoms and molecules, as well as by electronic transitions within atoms and molecules. The receivers or detectors of light largely utilize electronic transitions. We say the atoms and molecules are excited when they absorb and relax when they emit through electronic transitions. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Ultraviolet Radiation | Ultraviolet means “above violet.” The electromagnetic frequencies of ultraviolet radiation (UV) extend upward from violet, the highest-frequency visible light. Ultraviolet is also produced by atomic and molecular motions and electronic transitions. The wavelengths of ultraviolet extend from 400 nm down to about 10 nm at its highest frequencies, which overlap with the lowest X-ray frequencies. It was recognized as early as 1801 by Johann Ritter that the solar spectrum had an invisible component beyond the violet range. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Human Exposure to UV Radiation | It is largely exposure to UV-B that causes skin cancer. It is estimated that as many as 20% of adults will develop skin cancer over the course of their lifetime. Again, treatment is often successful if caught early. Despite very little UV-B reaching the Earth’s surface, there are substantial increases in skin-cancer rates in countries such as Australia, indicating how important it is that UV-B and UV-C continue to be absorbed by the upper atmosphere. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | UV Light and the Ozone Layer | If all of the Sun’s ultraviolet radiation reached the Earth’s surface, there would be extremely grave effects on the biosphere from the severe cell damage it causes. However, the layer of ozone (${\text{O}}_{3}$) in our upper atmosphere (10 to 50 km above the Earth) protects life by absorbing most of the dangerous UV radiation. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Benefits of UV Light | Besides the adverse effects of ultraviolet radiation, there are also benefits of exposure in nature and uses in technology. Vitamin D production in the skin (epidermis) results from exposure to UVB radiation, generally from sunlight. A number of studies indicate lack of vitamin D can result in the development of a range of cancers (prostate, breast, colon), so a certain amount of UV exposure is helpful. Lack of vitamin D is also linked to osteoporosis. Exposures (with no sunscreen) of 10 minutes a day to arms, face, and legs might be sufficient to provide the accepted dietary level. However, in the winter time north of about $\text{37º}$ latitude, most UVB gets blocked by the atmosphere. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | X-Rays | In the 1850s, scientists (such as Faraday) began experimenting with high-voltage electrical discharges in tubes filled with rarefied gases. It was later found that these discharges created an invisible, penetrating form of very high frequency electromagnetic radiation. This radiation was called an X-ray, because its identity and nature were unknown. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Gamma Rays | Soon after nuclear radioactivity was first detected in 1896, it was found that at least three distinct types of radiation were being emitted. The most penetrating nuclear radiation was called a gamma ray **($\gamma$ ray)** (again a name given because its identity and character were unknown), and it was later found to be an extremely high frequency electromagnetic wave. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | The Electromagnetic Spectrum | m42444 | Detecting Electromagnetic Waves from Space | The entire electromagnetic spectrum is used by researchers for investigating stars, space, and time. Arthur B. C. Walker was a pioneer in X-ray and ultraviolet observations, and designed specialized telescopes and instruments to observe the Sun’s atmosphere and corona. His developments significantly advanced our understanding of stars, and some of his developments are currently in use in space telescopes as well as in microchip manufacturing. As noted earlier, Penzias and Wilson detected microwaves to identify the background radiation originating from the Big Bang. Radio telescopes such as the Arecibo Radio Telescope in Puerto Rico and Parkes Observatory in Australia were designed to detect radio waves. |
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College Physics for AP® Courses 2e | Electromagnetic Waves | Energy in Electromagnetic Waves | m42446 | |||
College Physics for AP® Courses 2e | Geometric Optics | Connection for AP® Courses | m55436 | |||
College Physics for AP® Courses 2e | Geometric Optics | The Ray Aspect of Light | m42452 | |||
College Physics for AP® Courses 2e | Geometric Optics | The Law of Reflection | m42456 | |||
College Physics for AP® Courses 2e | Geometric Optics | The Law of Refraction | m42459 | The Speed of Light | Early attempts to measure the speed of light, such as those made by Galileo, determined that light moved extremely fast, perhaps instantaneously. The first real evidence that light traveled at a finite speed came from the Danish astronomer Ole Roemer in the late 17th century. Roemer had noted that the average orbital period of one of Jupiter’s moons, as measured from Earth, varied depending on whether Earth was moving toward or away from Jupiter. He correctly concluded that the apparent change in period was due to the change in distance between Earth and Jupiter and the time it took light to travel this distance. From his 1676 data, a value of the speed of light was calculated to be $2\text{.}\text{26}×{\text{10}}^{8}{\rule{0.25em}{0ex}}\text{m/s}$ (only 25% different from today’s accepted value). In more recent times, physicists have measured the speed of light in numerous ways and with increasing accuracy. One particularly direct method, used in 1887 by the American physicist Albert Michelson (1852–1931), is illustrated in [link]. Light reflected from a rotating set of mirrors was reflected from a stationary mirror 35 km away and returned to the rotating mirrors. The time for the light to travel can be determined by how fast the mirrors must rotate for the light to be returned to the observer’s eye. |
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College Physics for AP® Courses 2e | Geometric Optics | The Law of Refraction | m42459 | Law of Refraction | [link] shows how a ray of light changes direction when it passes from one medium to another. As before, the angles are measured relative to a perpendicular to the surface at the point where the light ray crosses it. (Some of the incident light will be reflected from the surface, but for now we will concentrate on the light that is transmitted.) The change in direction of the light ray depends on how the speed of light changes. The change in the speed of light is related to the indices of refraction of the media involved. In the situations shown in [link], medium 2 has a greater index of refraction than medium 1. This means that the speed of light is less in medium 2 than in medium 1. Note that as shown in [link](a), the direction of the ray moves closer to the perpendicular when it slows down. Conversely, as shown in [link](b), the direction of the ray moves away from the perpendicular when it speeds up. The path is exactly reversible. In both cases, you can imagine what happens by thinking about pushing a lawn mower from a footpath onto grass, and vice versa. Going from the footpath to grass, the front wheels are slowed and pulled to the side as shown. This is the same change in direction as for light when it goes from a fast medium to a slow one. When going from the grass to the footpath, the front wheels can move faster and the mower changes direction as shown. This, too, is the same change in direction as for light going from slow to fast. |
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College Physics for AP® Courses 2e | Geometric Optics | Total Internal Reflection | m42462 | Fiber Optics: Endoscopes to Telephones | Fiber optics is one application of total internal reflection that is in wide use. In communications, it is used to transmit telephone, internet, and cable TV signals. Fiber optics employs the transmission of light down fibers of plastic or glass. Because the fibers are thin, light entering one is likely to strike the inside surface at an angle greater than the critical angle and, thus, be totally reflected (See [link].) The index of refraction outside the fiber must be smaller than inside, a condition that is easily satisfied by coating the outside of the fiber with a material having an appropriate refractive index. In fact, most fibers have a varying refractive index to allow more light to be guided along the fiber through total internal refraction. Rays are reflected around corners as shown, making the fibers into tiny light pipes. |
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College Physics for AP® Courses 2e | Geometric Optics | Total Internal Reflection | m42462 | Corner Reflectors and Diamonds | A light ray that strikes an object consisting of two mutually perpendicular reflecting surfaces is reflected back exactly parallel to the direction from which it came. This is true whenever the reflecting surfaces are perpendicular, and it is independent of the angle of incidence. Such an object, shown in [link], is called a corner reflector, since the light bounces from its inside corner. Many inexpensive reflector buttons on bicycles, cars, and warning signs have corner reflectors designed to return light in the direction from which it originated. It was more expensive for astronauts to place one on the moon. Laser signals can be bounced from that corner reflector to measure the gradually increasing distance to the moon with great precision. |
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College Physics for AP® Courses 2e | Geometric Optics | Total Internal Reflection | m42462 | The Sparkle of Diamonds | Total internal reflection, coupled with a large index of refraction, explains why diamonds sparkle more than other materials. The critical angle for a diamond-to-air surface is only $\text{24}\text{.}4º$, and so when light enters a diamond, it has trouble getting back out. (See [link].) Although light freely enters the diamond, it can exit only if it makes an angle less than $\text{24}\text{.}4º$. Facets on diamonds are specifically intended to make this unlikely, so that the light can exit only in certain places. Good diamonds are very clear, so that the light makes many internal reflections and is concentrated at the few places it can exit—hence the sparkle. (Zircon is a natural gemstone that has an exceptionally large index of refraction, but not as large as diamond, so it is not as highly prized. Cubic zirconia is manufactured and has an even higher index of refraction ($\approx 2.17$), but still less than that of diamond.) The colors you see emerging from a sparkling diamond are not due to the diamond’s color, which is usually nearly colorless. Those colors result from dispersion, the topic of Dispersion: The Rainbow and Prisms. Colored diamonds get their color from structural defects of the crystal lattice and the inclusion of minute quantities of graphite and other materials. The Argyle Mine in Western Australia produces around 90% of the world’s pink, red, champagne, and cognac diamonds, while around 50% of the world’s clear diamonds come from central and southern Africa. |
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College Physics for AP® Courses 2e | Geometric Optics | Dispersion: The Rainbow and Prisms | m42466 | |||
College Physics for AP® Courses 2e | Geometric Optics | Image Formation by Lenses | m42470 | Ray Tracing and Thin Lenses | Ray tracing is the technique of determining or following (tracing) the paths that light rays take. For rays passing through matter, the law of refraction is used to trace the paths. Here we use ray tracing to help us understand the action of lenses in situations ranging from forming images on film to magnifying small print to correcting nearsightedness. While ray tracing for complicated lenses, such as those found in sophisticated cameras, may require computer techniques, there is a set of simple rules for tracing rays through thin lenses. A thin lens is defined to be one whose thickness allows rays to refract, as illustrated in [link], but does not allow properties such as dispersion and aberrations. An ideal thin lens has two refracting surfaces but the lens is thin enough to assume that light rays bend only once. A thin symmetrical lens has two focal points, one on either side and both at the same distance from the lens. (See [link].) Another important characteristic of a thin lens is that light rays through its center are deflected by a negligible amount, as seen in [link]. |
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College Physics for AP® Courses 2e | Geometric Optics | Image Formation by Lenses | m42470 | Image Formation by Thin Lenses | In some circumstances, a lens forms an obvious image, such as when a movie projector casts an image onto a screen. In other cases, the image is less obvious. Where, for example, is the image formed by eyeglasses? We will use ray tracing for thin lenses to illustrate how they form images, and we will develop equations to describe the image formation quantitatively. |
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College Physics for AP® Courses 2e | Geometric Optics | Image Formation by Lenses | m42470 | Problem-Solving Strategies for Lenses | Step 1. Examine the situation to determine that image formation by a lens is involved. |
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College Physics for AP® Courses 2e | Geometric Optics | Image Formation by Mirrors | m42474 | Problem-Solving Strategy for Mirrors | Step 1. Examine the situation to determine that image formation by a mirror is involved. |
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College Physics for AP® Courses 2e | Vision and Optical Instruments | Connection for AP® Courses | m55444 | |||
College Physics for AP® Courses 2e | Vision and Optical Instruments | Physics of the Eye | m42482 | |||
College Physics for AP® Courses 2e | Vision and Optical Instruments | Vision Correction | m42484 | |||
College Physics for AP® Courses 2e | Vision and Optical Instruments | Color and Color Vision | m42487 | Simple Theory of Color Vision | We have already noted that color is associated with the wavelength of visible electromagnetic radiation. When our eyes receive pure-wavelength light, we tend to see only a few colors. Six of these (most often listed) are red, orange, yellow, green, blue, and violet. These are the rainbow of colors produced when white light is dispersed according to different wavelengths. There are thousands of other hues that we can perceive. These include brown, teal, gold, pink, and white. One simple theory of color vision implies that all these hues are our eye’s response to different combinations of wavelengths. This is true to an extent, but we find that color perception is even subtler than our eye’s response for various wavelengths of light. |
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College Physics for AP® Courses 2e | Vision and Optical Instruments | Color and Color Vision | m42487 | Color Constancy and a Modified Theory of Color Vision | The eye-brain color-sensing system can, by comparing various objects in its view, perceive the true color of an object under varying lighting conditions—an ability that is called color constancy. We can sense that a white tablecloth, for example, is white whether it is illuminated by sunlight, fluorescent light, or candlelight. The wavelengths entering the eye are quite different in each case, as the graphs in [link] imply, but our color vision can detect the true color by comparing the tablecloth with its surroundings. |
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College Physics for AP® Courses 2e | Vision and Optical Instruments | Microscopes | m42491 | |||
College Physics for AP® Courses 2e | Vision and Optical Instruments | Telescopes | m42493 | |||
College Physics for AP® Courses 2e | Vision and Optical Instruments | Aberrations | m42292 | |||
College Physics for AP® Courses 2e | Wave Optics | Connection for AP® Courses | m55362 | |||
College Physics for AP® Courses 2e | Wave Optics | The Wave Aspect of Light: Interference | m42501 | |||
College Physics for AP® Courses 2e | Wave Optics | Huygens's Principle: Diffraction | m42505 | |||
College Physics for AP® Courses 2e | Wave Optics | Young’s Double Slit Experiment | m42508 | |||
College Physics for AP® Courses 2e | Wave Optics | Multiple Slit Diffraction | m42512 | |||
College Physics for AP® Courses 2e | Wave Optics | Single Slit Diffraction | m42515 | |||
College Physics for AP® Courses 2e | Wave Optics | Limits of Resolution: The Rayleigh Criterion | m42517 | |||
College Physics for AP® Courses 2e | Wave Optics | Thin Film Interference | m42519 | Problem-Solving Strategies for Wave Optics | **Step 1.** *Examine the situation to determine that interference is involved*. Identify whether slits or thin film interference are considered in the problem. |
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College Physics for AP® Courses 2e | Wave Optics | Polarization | m42522 | Polarization by Reflection | By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter. |
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College Physics for AP® Courses 2e | Wave Optics | Polarization | m42522 | Polarization by Scattering | If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. [link] helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in [link], there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations. |
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College Physics for AP® Courses 2e | Wave Optics | Polarization | m42522 | Liquid Crystals and Other Polarization Effects in Materials | While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by $\text{90º}$. Furthermore, this property can be turned off by the application of a voltage, as illustrated in [link]. It is possible to manipulate this characteristic quickly and in small well-defined regions to create the contrast patterns we see in so many LCD devices. |
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College Physics for AP® Courses 2e | Wave Optics | *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light | m42290 | |||
College Physics for AP® Courses 2e | Special Relativity | Connection for AP® Courses | m55094 | |||
College Physics for AP® Courses 2e | Special Relativity | Einstein’s Postulates | m42528 | Einstein’s First Postulate | The first postulate upon which Einstein based the theory of special relativity relates to reference frames. All velocities are measured relative to some frame of reference. For example, a car’s motion is measured relative to its starting point or the road it is moving over, a projectile’s motion is measured relative to the surface it was launched from, and a planet’s orbit is measured relative to the star it is orbiting around. The simplest frames of reference are those that are not accelerated and are not rotating. Newton’s first law, the law of inertia, holds exactly in such a frame. |
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