The 19th-century inventor Nikola Tesla proposed to transmit electric power via sinusoidal electromagnetic waves. Suppose power is to be transmitted in a beam of cross-sectional area 100 m2. What electric- and magnetic-field amplitudes are required to transmit an amount of power comparable to that handled by modern transmission lines (that carry voltages and currents of the order of 500 kV and 1000 A)?
> A beam of light is traveling inside a solid glass cube that has index of refraction 1.62. It strikes the surface of the cube from the inside. a. If the cube is in air, at what minimum angle with the normal inside the glass will this light not enter the
> The critical angle for total internal reflection at a liquid– air interface is 42.5°. a. If a ray of light traveling in the liquid has an angle of incidence at the interface of 35.0°, what angle does the refracted ray in the air make with the normal? b
> A beam of white light passes through a uniform thickness of air. If the intensity of the scattered light in the middle of the green part of the visible spectrum is I, find the intensity (in terms of I) of scattered light in the middle of a. the red part
> Three polarizing filters are stacked with the polarizing axes of the second and third at 45.0° and 90.0°, respectively, with that of the first. a. If unpolarized light of intensity I0 is incident on the stack, find the intensity and state of polarizatio
> Unpolarized light of intensity 20.0 W/cm2 is incident on two polarizing filters. The axis of the first filter is at an angle of 25.0° counterclockwise from the vertical (viewed in the direction the light is traveling), and the axis of the second filter i
> In an L-R-C series circuit, R = 400 Ω, L = 0.350 H, and C = 0.0120 µF. a. What is the resonance angular frequency of the circuit? b. The capacitor can withstand a peak voltage of 670 V. If the voltage source operates at the resonance frequency, what ma
> In an L-R-C series circuit, R = 150 Ω, L = 0.750 H, and C = 0.0180 µF. The source has voltage amplitude V = 150 V and a frequency equal to the resonance frequency of the circuit. a. What is the power factor? b. What is the average power delivered by th
> An L-R-C series circuit consists of a source with voltage amplitude 120 V and angular frequency 50.0 rad/s, a resistor with R = 400 Ω, an inductor with L = 3.00 H, and a capacitor with capacitance C. a. For what value of C will the current amplitude in
> Give several examples of electromagnetic waves that are encountered in everyday life. How are they all alike? How do they differ?
> A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of θa = 36.2°, the ray refracted into the water makes an an
> Light of original intensity I0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I0/10. a. If the original light is unpo
> You have a 200-Ω resistor, a 0.400-H inductor, a 5.00-µF capacitor, and a variable frequency ac source with an amplitude of 3.00 V. You connect all four elements together to form a series circuit. a. At what frequency will the current in the circuit be
> In an L-R-C series circuit the source is operated at its resonant angular frequency. At this frequency, the reactance XC of the capacitor is 200 Ω and the voltage amplitude across the capacitor is 600 V. The circuit has R = 300 Ω. What is the voltage amp
> A series ac circuit contains a 250-Ω resistor, a 15-mH inductor, a 3.5-µF capacitor, and an ac power source of voltage amplitude 45 V operating at an angular frequency of 360 rad/s. a. What is the power factor of this circuit? b. Find the average power
> For a certain sinusoidal wave of intensity I, the amplitude of the magnetic field is B. What would be the amplitude (in terms of B) in a similar wave of twice the intensity?
> Is polarization a property of all electromagnetic waves, or is it unique to visible light? Can sound waves be polarized? What fundamental distinction in wave properties is involved? Explain.
> A light source radiates a sinusoidal electromagnetic wave uniformly in all directions. This wave exerts an average pressure p on a perfectly reflecting surface a distance R away from it. What average pressure (in terms of p) would this wave exert on a pe
> If a light beam carries momentum, should a person holding a flashlight feel a recoil analogous to the recoil of a rifle when it is fired? Why is this recoil not actually observed?
> By measuring the electric and magnetic fields at a point in space where there is an electromagnetic wave, can you determine the direction from which the wave came? Explain.
> In an ac circuit, why is the average power for an inductor and a capacitor zero, but not for a resistor?
> When hot air rises from a radiator or heating duct, objects behind it appear to shimmer or waver. What causes this?
> In Fig. 33.31, since the light that is scattered out of the incident beam is polarized, why is the transmitted beam not also partially polarized? From Fig. 33.31 33.31 When the sunbathing observer on the left looks up, he sees blue, polarized sunli
> When unpolarized light is incident on two crossed polarizers, no light is transmitted. A student asserted that if a third polarizer is inserted between the other two, some transmission will occur. Does this make sense? How can adding a third filter incre
> Public television station KQED in San Francisco broadcasts a sinusoidal radio signal at a power of 777 kW. Assume that the wave spreads out uniformly into a hemisphere above the ground. At a home 5.00 km away from the antenna, a. what average pressure d
> When a sheet of plastic food wrap is placed between two crossed polarizers, no light is transmitted. When the sheet is stretched in one direction, some light passes through the crossed polarizers. What is happening?
> Does it make sense to talk about the polarization of a longitudinal wave, such as a sound wave? Why or why not?
> Huygens’s principle also applies to sound waves. During the day, the temperature of the atmosphere decreases with increasing altitude above the ground. But at night, when the ground cools, there is a layer of air just above the surface in which the tempe
> The explanation given in Section 33.6 for the color of the setting sun should apply equally well to the rising sun, since sunlight travels the same distance through the atmosphere to reach your eyes at either sunrise or sunset. Typically, however, sunset
> Atmospheric haze is due to water droplets or smoke particles (“smog”). Such haze reduces visibility by scattering light, so that the light from distant objects becomes randomized and images become indistinct. Explain why visibility through haze can be im
> Light scattered from blue sky is strongly polarized because of the nature of the scattering process described in Section 33.6. But light scattered from white clouds is usually not polarized. Why not?
> A salesperson at a bargain counter claims that a certain pair of sunglasses has Polaroid filters; you suspect that the glasses are just tinted plastic. How could you find out for sure?
> When driving on the upper level of the Bay Bridge, westbound from Oakland to San Francisco, you can easily pick up a number of radio stations on your car radio. But when driving eastbound on the lower level of the bridge, which has steel girders on eithe
> You want to double the resonance angular frequency of an L-R-C series circuit by changing only the pertinent circuit elements all by the same factor. a. Which ones should you change? b. By what factor should you change them?
> When light is incident on an interface between two materials, the angle of the refracted ray depends on the wavelength, but the angle of the reflected ray does not. Why should this be?
> An L-R-C series circuit with L = 0.120 H, R = 240 Ω, and C = 7.30 µF carries an rms current of 0.450 A with a frequency of 400 Hz. a. What are the phase angle and power factor for this circuit? b. What is the impedance of the circuit? c. What is the r
> An ideal transformer has N1 windings in the primary and N2 windings in its secondary. If you double only the number of secondary windings, by what factor does a. the voltage amplitude in the secondary change, and b. the effective resistance of the seco
> Can a transformer be used with dc? Explain. What happens if a transformer designed for 120-V ac is connected to a 120-V dc line?
> A circuit consists of a light bulb, a capacitor, and an inductor connected in series to an ac source. Is it possible for both the capacitor and the inductor to be removed and the brightness of the bulb to remain the same? Explain.
> Light requires about 8 minutes to travel from the sun to the earth. Is it delayed appreciably by the earth’s atmosphere? Explain.
> A coil of wire wrapped on a hollow tube and a light bulb are connected in series to an ac source. What happens to the brightness of the bulb when an iron rod is inserted in the tube?
> A light bulb and a parallel-plate capacitor with air between the plates are connected in series to an ac source. What happens to the brightness of the bulb when a dielectric is inserted between the plates of the capacitor? Explain.
> In Example 31.6 (Section 31.4), a hair dryer is treated as a pure resistor. But because there are coils in the heating element and in the motor that drives the blower fan, a hair dryer also has inductance. Qualitatively, does including an inductance incr
> Most automobiles have vertical antennas for receiving radio broadcasts. Explain what this tells you about the direction of polarization of E in the radio waves used in broadcasting.
> Household electric power in most of western Europe is supplied at 240 V, rather than the 120 V that is standard in the United States and Canada. What are the advantages and disadvantages of each system?
> In an L-R-C series circuit, the source has a voltage amplitude of 120 V, R = 80.0 Ω, and the reactance of the capacitor is 480 Ω. The voltage amplitude across the capacitor is 360 V. a. What is the current amplitude in the circuit? b. What is the imped
> a. Use the results of part (a) of Exercise 31.21 to show that the average power delivered by the source in an L-R-C series circuit is given by Pav = I2 rms R. b. An L-R-C series circuit has R = 96.0 Ω, and the amplitude of the voltage across the resisto
> An L-R-C series circuit has R = 60.0 Ω, L = 0.800 H, and C = 3.00 * 10-4 F. The ac source has voltage amplitude 90.0 V and angular frequency 120 rad/s. a. What is the maximum energy stored in the inductor? b. When the energy stored in the inductor is a
> An L-R-C series circuit consists of a 2.50-µF capacitor, a 5.00-mH inductor, and a 75.0-Ω resistor connected across an ac source of voltage amplitude 15.0 V having variable frequency. a. Under what circumstances is the average power delivered to the cir
> Interplanetary space contains many small particles referred to as interplanetary dust. Radiation pressure from the sun sets a lower limit on the size of such dust particles. To see the origin of this limit, consider a spherical dust particle of radius R
> A cylindrical conductor with a circular cross section has a radius a and a resistivity ρ and carries a constant current I. a. What are the magnitude and direction of the electric field vector E at a point just inside the wire at a distance a from the ax
> In an L-R-C series circuit, the phase angle is 40.0°, with the source voltage leading the current. The reactance of the capacitor is 400 Ω, and the resistance of the resistor is 200 Ω. The average power delivered by the source is 150 W. Find a. the reac
> In an L-R-C series circuit the magnitude of the phase angle is 54.0°, with the source voltage lagging the current. The reactance of the capacitor is 350 Ω, and the resistor resistance is 180 Ω. The average power delivered by the source is 140 W. Find a.
> In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0 ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the
> Because the speed of light in vacuum (or air) has such a large value, it is very difficult to measure directly. To measure this speed, you conduct an experiment in which you measure the amplitude of the electric field in a laser beam as you change the in
> Physicians use high-frequency (f = 1-5 MHz) sound waves, called ultrasound, to image internal organs. The speed of these ultrasound waves is 1480 m/s in muscle and 344 m/s in air. We define the index of refraction of a material for sound waves to be the
> Light is incident along the normal on face AB of a glass prism of refractive index 1.52, as shown in Fig. E33.21. Find the largest value the angle a can have without any light refracted out of the prism at face AC if a. the prism is immersed in air and
> One application of L-R-C series circuits is to high-pass or lowpass filters, which filter out either the low- or high-frequency components of a signal. A high-pass filter is shown in Fig. P31.47, where the output voltage is taken across the L-R combinati
> At a frequency ω1 the reactance of a certain capacitor equals that of a certain inductor. a. If the frequency is changed to ω2 = 2 ω1, what is the ratio of the reactance of the inductor to that of the capacitor? Which reactance is larger? b. If the fre
> In an L-R-C series circuit, R = 300 Ω, XC = 300 Ω, and XL = 500 Ω. The average electrical power consumed in the resistor is 60.0 W. a. What is the power factor of the circuit? b. What is the rms voltage of the source?
> A large electromagnetic coil is connected to a 120-Hz ac source. The coil has resistance 400 Ω, and at this source frequency the coil has inductive reactance 250 Ω. a. What is the inductance of the coil? b. What must the rms voltage of the source be if
> A glass plate 2.50 mm thick, with an index of refraction of 1.40, is placed between a point source of light with wavelength 540 nm (in vacuum) and a screen. The distance from source to screen is 1.80 cm. How many wavelengths are there between the source
> A toroidal solenoid has 2900 closely wound turns, cross-sectional area 0.450 cm2, mean radius 9.00 cm, and resistance R = 2.80 Ω. Ignore the variation of the magnetic field across the cross section of the solenoid. What is the amplitude of the current in
> A parallel-plate capacitor having square plates 4.50 cm on each side and 8.00 mm apart is placed in series with the following: an ac source of angular frequency 650 rad/s and voltage amplitude 22.5 V; a 75.0-Ω resistor; and an ideal solenoid that is 9.00
> Five infinite-impedance voltmeters, calibrated to read rms values, are connected as shown in Fig. P31.40. Let R = 200 Ω, L = 0.400 H, C = 6.00 µF, and V = 30.0 V. What is the reading of each voltmeter if a. v = 200 rad/s
> An L-R-C series circuit has C = 4.80 µF, L = 0.520 H, and source voltage amplitude V = 56.0 V. The source is operated at the resonance frequency of the circuit. If the voltage across the capacitor has amplitude 80.0 V, what is the value of R for the resi
> A small helium–neon laser emits red visible light with a power of 5.80 mW in a beam of diameter 2.50 mm. a. What are the amplitudes of the electric and magnetic fields of this light? b. What are the average energy densities associated with the electric
> In an L-R-C series circuit, the components have the following values: L = 20.0 mH, C = 140 nF, and R = 350 Ω. The generator has an rms voltage of 120 V and a frequency of 1.25 kHz. Determine a. the power supplied by the generator and b. the power dissi
> Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of the wave? a. E in the +x-direction, B in the +y-direction; b. E in the -y-direction, B in the +x-direction; c. E in the +z
> If the frequency at which the electrode is oscillated is increased to a very large value, the electrode’s impedance a. approaches infinity; b. approaches zero; c. approaches a constant but nonzero value; d. does not change.
> The signal from the oscillating electrode is fed into an amplifier, which reports the measured voltage as an rms value, 1.5 nV. What is the potential difference between the two extremes? a. 1.5 nV; b. 3.0 nV; c. 2.1 nV; d. 4.2 nV.
> If the electrode oscillates between two points 20 µm apart at a frequency of (5000/π)Hz, what is the electrode’s impedance? a. 0; b. infinite; c. 2 * 104 Ω; d. 2 * 106 Ω.
> What is the dc impedance of the electrode, assuming that it behaves as an ideal capacitor? a. 0; b. infinite; c. 2 * 104 Ω; d. 2 * 106 Ω.
> A coil has a resistance of 48.0 Ω. At a frequency of 80.0 Hz the voltage across the coil leads the current in it by 52.3°. Determine the inductance of the coil.
> For a sinusoidal electromagnetic wave in vacuum, such as that described by Eq. (32.16), show that the average energy density in the electric field is the same as that in the magnetic field.
> A satellite 575 km above the earth’s surface transmits sinusoidal electromagnetic waves of frequency 92.4 MHz uniformly in all directions, with a power of 25.0 kW. a. What is the intensity of these waves as they reach a receiver at the surface of the ea
> You are analyzing an ac circuit that contains a solenoid and a capacitor in series with an ac source that has voltage amplitude 90.0 V and angular frequency ω. For different capacitors in the circuit, each with known capacitance, you measure t
> Consider a sinusoidal electromagnetic wave with fields E = Emax
> An L-R-C series circuit draws 220 W from a 120-V (rms), 50.0-Hz ac line. The power factor is 0.560, and the source voltage leads the current. a. What is the net resistance R of the circuit? b. Find the capacitance of the series capacitor that will resu
> A ray of light is traveling in a glass cube that is totally immersed in water. You find that if the ray is incident on the glass– water interface at an angle to the normal larger than 48.7°, no light is refracted into the water. What is the refractive in
> Consider an L-R-C series circuit with a 1.80-H inductor, a 0.900-µF capacitor, and a 300-Ω resistor. The source has terminal rms voltage Vrms = 60.0 V and variable angular frequency ω. a. What is the resonance angular frequency ω0 of the circuit? b. Wh
> A resistance R, capacitance C, and inductance L are connected in series to a voltage source with amplitude V and variable angular frequency ω. If ω = ω0, the resonance angular frequency, find a. the maximum current in the resistor; b. the maximum volta
> Doubling the frequency of a wave in the range of 25 Hz to 3 kHz represents what change in the maximum allowed electromagnetic-wave intensity? a. A factor of 2; b. a factor of 1/ 2 ; c. a factor of 1/2 ; d. a factor of 1/4 .
> In the United States, household electrical power is provided at a frequency of 60 Hz, so electromagnetic radiation at that frequency is of particular interest. On the basis of the ICNIRP guidelines, what is the maximum intensity of an electromagnetic wav
> Consider electromagnetic waves propagating in air. a. Determine the frequency of a wave with a wavelength of i. 5.0 km, ii. 5.0 µm, iii. 5.0 nm. b. What is the wavelength (in meters and nanometers) of i. gamma rays of frequency 6.50 * 1021 Hz and
> A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 µT and a wavelength of 432 nm is traveling in the +x-direction through empty space. a. What is the frequency of this wave? b. What is the amplitude of the associat
> There are two categories of ultraviolet light. Ultraviolet A (UVA) has a wavelength ranging from 320 nm to 400 nm. It is necessary for the production of vitamin D. UVB, with a wavelength in vacuum between 280 nm and 320 nm, is more dangerous because it i
> Consider each of the following electric- and magnetic field orientations. In each case, what is the direction of propagation of the wave? a. E = E
> A sinusoidal electromagnetic wave is propagating in vacuum in the +z-direction. If at a particular instant and at a certain point in space the electric field is in the +x-direction and has magnitude 4.00 V/m, what are the magnitude and direction of the m
> He–Ne lasers are often used in physics demonstrations. They produce light of wavelength 633 nm and a power of 0.500 mW spread over a cylindrical beam 1.00 mm in diameter (although these quantities can vary). a. What is the intensity of this laser beam?
> A resistor with R = 300 Ω and an inductor are connected in series across an ac source that has voltage amplitude 500 V. The rate at which electrical energy is dissipated in the resistor is 286 W. What is a. the impedance Z of the circuit; b. the amplit
> A laser beam has diameter 1.20 mm. What is the amplitude of the electric field of the electromagnetic radiation in this beam if the beam exerts a force of 3.8 * 10-9 N on a totally reflecting surface?
> The intensity of a cylindrical laser beam is 0.800 W/m2. The cross-sectional area of the beam is 3.0 * 10-4 m2 and the intensity is uniform across the cross section of the beam. a. What is the average power output of the laser? b. What is the rms value
> A space probe 2.0 * 1010 m from a star measures the total intensity of electromagnetic radiation from the star to be 5.0 * 103 W/m2. If the star radiates uniformly in all directions, what is its total average power output?
> An electromagnetic wave has a magnetic field given by B (x, t) = -(8.25 * 10-9 T)
> An electromagnetic wave has an electric field given by E (y, t) = (3.10 * 105 V/m)
> Light traveling in air is incident on the surface of a block of plastic at an angle of 62.7° to the normal and is bent so that it makes a 48.1° angle with the normal in the plastic. Find the speed of light in the plastic.
> Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?
> A light beam travels at 1.94 * 108 m/s in quartz. The wavelength of the light in quartz is 355 nm. a. What is the index of refraction of quartz at this wavelength? b. If this same light travels through air, what is its wavelength there?
> Light with a frequency of 5.80 * 1014 Hz travels in a block of glass that has an index of refraction of 1.52. What is the wavelength of the light a. in vacuum and b. in the glass
> The refractive index of a certain glass is 1.66. For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in a. air and b. water?
