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
> 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
> 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 tra
> 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
> 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?
> We can reasonably model a 75-W incandescent light bulb as a sphere 6.0 cm in diameter. Typically, only about 5% of the energy goes to visible light; the rest goes largely to nonvisible infrared radiation. a. What is the visible-light intensity (in W/m2)
> A beam of light has a wavelength of 650 nm in vacuum. a. What is the speed of this light in a liquid whose index of refraction at this wavelength is 1.47? b. What is the wavelength of these waves in the liquid?
> A parallel beam of unpolarized light in air is incident at an angle of 54.5° (with respect to the normal) on a plane glass surface. The reflected beam is completely linearly polarized. a. What is the refractive index of the glass? b. What is the angle
> A beam of light strikes a sheet of glass at an angle of 57.0° with the normal in air. You observe that red light makes an angle of 38.1° with the normal in the glass, while violet light makes a 36.7° angle. a. What are the indexes of refraction of this
> The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as measured in air. This light travels through the vitreous h
> Light enters a solid pipe made of plastic having an index of refraction of 1.60. The light travels parallel to the upper part of the pipe (Fig. E33.15). You want to cut the face AB so that all the light will reflect back into the pipe after it first stri
> A ray of light traveling in water is incident on an interface with a flat piece of glass. The wavelength of the light in the water is 726 nm, and its wavelength in the glass is 544 nm. If the ray in water makes an angle of 56.0° with respect to the norma
> A transformer connected to a 120-V (rms) ac line is to supply 13,000 V (rms) for a neon sign. To reduce shock hazard, a fuse is to be inserted in the primary circuit; the fuse is to blow when the rms current in the secondary circuit exceeds 8.50 mA. a.
> A transformer connected to a 120-V (rms) ac line is to supply 12.0 V (rms) to a portable electronic device. The load resistance in the secondary is 5.00 Ω. a. What should the ratio of primary to secondary turns of the transformer be? b. What rms curren
> You plan to take your hair dryer to Europe, where the electrical outlets put out 240 V instead of the 120 V seen in the United States. The dryer puts out 1600 W at 120 V. a. What could you do to operate your dryer via the 240-V line in Europe? b. What
> In an L-R-C series circuit, L = 0.280 H and C = 4.00µF. The voltage amplitude of the source is 120 V. a. What is the resonance angular frequency of the circuit? b. When the source operates at the resonance angular frequency, the current amplitude in th
> A 200-Ω resistor, 0.900-H inductor, and 6.00-µF capacitor are connected in series across a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. a. What are v, vR, vL, and vC at t = 20.0 ms? Compare vR + vL + vC to v at
> An electromagnetic standing wave in air has frequency 75.0 MHz. a. What is the distance between nodal planes of the E field? b. What is the distance between a nodal plane of E and the closest nodal plane of B?
> A ray of light is incident on a plane surface separating two sheets of glass with refractive indexes 1.70 and 1.58. The angle of incidence is 62.0°, and the ray originates in the glass with n = 1.70. Compute the angle of refraction.
> A standing electromagnetic wave in a certain material has frequency 2.20 * 1010 Hz. The nodal planes of B are 4.65 mm apart. Find a. the wavelength of the wave in this material; b. the distance between adjacent nodal planes of the E field; c. the spee
> In an L-R-C series circuit, R = 300 Ω, L = 0.400 H, and C = 6.00 * 10-8 F. When the ac source operates at the resonance frequency of the circuit, the current amplitude is 0.500 A. a. What is the voltage amplitude of the source? b. What is the amplitude
> An L-R-C series circuit is constructed using a 175-Ω resistor, a 12.5-µF capacitor, and an 8.00-mH inductor, all connected across an ac source having a variable frequency and a voltage amplitude of 25.0 V. a. At what angular frequency will the impedance
> If the eye receives an average intensity greater than 1.0 * 102 W/m2, damage to the retina can occur. This quantity is called the damage threshold of the retina. a. What is the largest average power (in mW) that a laser beam 1.5 mm in diameter can have
> In the 25-ft Space Simulator facility at NASA’s Jet Propulsion Laboratory, a bank of overhead arc lamps can produce light of intensity 2500 W/m2 at the floor of the facility. (This simulates the intensity of sunlight near the planet Venus.) Find the aver
> An intense light source radiates uniformly in all directions. At a distance of 5.0 m from the source, the radiation pressure on a perfectly absorbing surface is 9.0 * 10-6 Pa. What is the total average power output of the source?
> An L-R-C series circuit is connected to a 120-Hz ac source that has Vrms = 80.0 V. The circuit has a resistance of 75.0 Ω and an impedance at this frequency of 105 Ω. What average power is delivered to the circuit by the source?
> A monochromatic light source with power output 60.0 W radiates light of wavelength 700 nm uniformly in all directions. Calculate Emax and Bmax for the 700-nm light at a distance of 5.00 m from the source.
> The resistor, inductor, capacitor, and voltage source described in Exercise 31.14 are connected to form an L-R-C series circuit. a. What is the impedance of the circuit? b. What is the current amplitude? c. What is the phase angle of the source voltag
> A sinusoidal electromagnetic wave emitted by a cellular phone has a wavelength of 35.4 cm and an electric-field amplitude of 5.40 * 10-2 V/m at a distance of 250 m from the phone. Calculate a. the frequency of the wave; b. the magnetic-field amplitude;
> a. Show that for an L-R-C series circuit the power factor is equal to R/Z. b. An L-R-C series circuit has phase angle -31.5o. The voltage amplitude of the source is 90.0 V. What is the voltage amplitude across the resistor?
> The energy flow to the earth from sunlight is about 1.4 kW/m2. a. Find the maximum values of the electric and magnetic fields for a sinusoidal wave of this intensity. b. The distance from the earth to the sun is about 1.5 * 1011 m. Find the total power
> The power of a certain CD player operating at 120 V rms is 20.0 W. Assuming that the CD player behaves like a pure resistor, find a. the maximum instantaneous power; b. the rms current; c. the resistance of this player.
> A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area 0.500 m2. At the window, the electric field of the wave has rms value 0.0400 V/m. How much energy does this wave carry through the window d
> In an L-R-C series circuit, the rms voltage across the resistor is 30.0 V, across the capacitor it is 90.0 V, and across the inductor it is 50.0 V. What is the rms voltage of the source?
> A horizontal, parallel- sided plate of glass having a refractive index of 1.52 is in contact with the surface of water in a tank. A ray coming from above in air makes an angle of incidence of 35.0° with the normal to the top surface of the glass. a. Wha
> An electromagnetic wave with frequency 5.70 * 1014 Hz propagates with a speed of 2.17 * 108 m/s in a certain piece of glass. Find a. the wavelength of the wave in the glass; b. the wavelength of a wave of the same frequency propagating in air; c. the
> An electromagnetic wave with frequency 65.0 Hz travels in an insulating magnetic material that has dielectric constant 3.64 and relative permeability 5.18 at this frequency. The electric field has amplitude 7.20 * 10-3 V/m. a. What is the speed of propa
> A 150-Ω resistor is connected in series with a 0.250-H inductor and an ac source. The voltage across the resistor is vR =(3.80 V)cos[(720 rad/s)t]. a. Derive an expression for the circuit current. b. Determine the inductive reactance of the inductor.
> You have a 200-Ω resistor, a 0.400-H inductor, and a 6.00-µF capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. a. What is the im
> A 250-Ω resistor is connected in series with a 4.80-µF capacitor and an ac source. The voltage across the capacitor is vC = (7.60 V)sin[(120 rad/s)t]. a. Determine the capacitive reactance of the capacitor. b. Derive an expression for the voltage vR ac
> A 0.180-H inductor is connected in series with a 90.0-Ω resistor and an ac source. The voltage across the inductor is vL = -(12.0 V)sin[(480 rad/s)t]. a. Derive an expression for the voltage vR across the resistor. b. What is vR at t = 2.00 ms?
> You want the current amplitude through a 0.450-mH inductor (part of the circuitry for a radio receiver) to be 1.80 mA when a sinusoidal voltage with amplitude 12.0 V is applied across the inductor. What frequency is required?
> a. What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz? b. What is the inductance of an inductor whose reactance is 120 Ω at 80.0 Hz? c. What is the reactance of a 4.00-mF capacitor at a frequency of 80.0 Hz? d. What is the capacitanc
