Answer: The Metal DetectorMetal detectors use induced

Problem 1CQ The world’s strongest magnet can produce a steady field of 45 T. If a circular wire loop of radius 10 cm were held in th

Problem 1P A potential difference of 0.050 V is developed across the 10-cm-long wire in Figure P25.1 as it moves through a magnetic field at 5.0 m/s. The magnetic field is perpendicular to the axis of the wire. What are the direction and strength of the magnetic field?

Problem 2CQ The rapid vibration accompanying the swimming motions of mayflies has been measured by gluing a small magnet to a swimming mayfly and recording the emf in a small coil of wire placed nearby. Explain how this technique works.

Problem 2P A scalloped hammerhead shark swims at a steady speed of 1.5 m/s with its 85-cm-wide head perpendicular to the earth’s 50 ?T magnetic field. What is the magnitude of the emf induced between the two sides of the shark’s head?

Problem 3CQ Parts a through f of Figure Q25.3 show one or more metal wires sliding on fixed metal rails in a magnetic field. For each, determine if the induced current is clockwise, counterclockwise, or zero.

Problem 3P A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.20 ?. Pulling the wire with a force of 1.0 N causes 4.0 W of power to be dissipated in the circuit. a. What is the speed of the wire when pulled with a force of 1.0 N? b. What is the strength of the magnetic field?

Problem 4CQ Figure Q25.4 shows four different loops in a magnetic field. The numbers indicate the lengths of the sides and the strength of the field. Rank in order the magnetic fluxes , from the largest to the smallest. Some may be equal. Explain.

Problem 4P Figure P25.4 shows a 15-cm-long metal rod pulled along two frictionless, conducting rails at a constant speed of 3.5 m/s. The rails have negligible resistance, but the rod has a resistance of 0.65 ?. a. What is the current induced in the rod? b. What force is required to keep the rod moving at a constant speed?

Problem 5CQ Figure Q25.5 shows four different circular loops that are perpendicular to the page. The radius of loops 3 and 4 is twice that of loops 1 and 2. The magnetic field is the same for each. Rank in order the magnetic fluxes , from the largest to the smallest. Some may be equal. Explain.

Problem 5P A 50 g horizontal metal bar, 12 cm long, is free to slide up and down between two tall, vertical metal rods that are 12 cm apart. A 0.060 T magnetic field is directed perpendicular to the plane of the rods. The bar is raised to near the top of the rods, and a 1.0 ? resistor is connected across the two rods at the top. Then the bar is dropped. What is the terminal speed at which the bar falls? Assume the bar remains horizontal and in contact with the rods at all times

Problem 6CQ A circular loop rotates at constant speed about an axle through the center of the loop. Figure Q25.6 shows an edge view and defines the angle ?, which increases from 0° to 360° as the loop rotates. a. At what angle or angles is the magnetic flux a maximum? b. At what angle or angles is the magnetic flux a minimum? c. At what angle or angles is the magnetic flux changing most rapidly?

Problem 6P A delivery truck with 2.8-m-high aluminum sides is driving west at 75 km/h in a region where the earth’s magnetic field is . a. What is the potential difference between the top and the bottom of the truck’s side panels? b. Will the tops of the panels be positive or negative relative to the bottoms?

Problem 8CQ The magnetic flux passing through a coil of wire varies as shown in Figure Q25.8. During which time interval(s) will an induced current be present in the coil? Explain.

Problem 7P Figure P25.9 is an edge-on view of a 10-cm-diameter circular loop rotating in a uniform 0.050 T magnetic field. What is the magnetic flux through the loop when ? is 0°, 30°, 60°, and 90°?

Problem 8P What is the magnetic flux through the loop shown in Figure P25.10?

Problem 7CQ The power lines that run through your neighborhood carry alternating currents that reverse direction 120 times per second. As the current changes, so does the magnetic field around a line. Suppose you wanted to put a loop of wire up near the power line to extract power by “tapping” the magnetic field. Sketch a picture of how you would orient the coil of wire next to a power line to develop the maximum emf in the coil. (Note that this is dangerous and illegal, and not something you should try.)

Problem 9CQ There is a counterclockwise induced current in the conducting loop shown in Figure Q25.9. Is the magnetic field inside the loop increasing in strength, decreasing in strength, or steady?

Problem 9P The 2.0-cm-diameter solenoid in Figure P25.11 passes through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.20 T. What is the magnetic flux through the loop (a) when it is perpendicular to the solenoid and (b) when it is tilted at a 60° angle?

Problem 10CQ Cars on the “Tower of Doom” carnival ride are dropped from a great height, giving riders a few seconds of free fall. To stop the cars, strong permanent magnets attached to the bottoms of the cars pass very close to aluminum vanes sticking up from the bottom of the track. Explain how this braking system works

Problem 10P At a typical location in the United States, the earth’s magnetic field has a magnitude of and is at a 65° angle from the horizontal. What is the flux through the 22 cm × 28 cm front cover of your textbook if it is flat on your desk?

Problem 11CQ A magnet dropped through a clear plastic tube accelerates as expected in free fall. If dropped through an aluminum tube of exactly the same length and diameter, the magnet falls much more slowly. Explain the behavior of the second magnet.

Problem 11P The metal equilateral triangle in Figure P25.13, 20 cm on each side, is halfway into a 0.10 T magnetic field. a. What is the magnetic flux through the triangle? b. If the magnetic field strength decreases, what is the direction of the induced current in the triangle?

Problem 12CQ The conducting loop in Figure Q25.11 is moving into the region between the magnetic poles shown. a. Is the induced current (viewed from above) clockwise or counterclockwise? b. Is there an attractive magnetic force that tends to pull the loop in, like a magnet pulls on a paper clip? Or do you need to push the loop in against a repulsive force?

Problem 12P Figure P25.17 shows a 10-cm-diameter loop in three different magnetic fields. The loop’s resistance is 0.10 ?. For each case, determine the induced emf, the induced current, and the direction of the current.

Problem 13P The plane of a loop of wire is perpendicular to a magnetic field. Rank, from greatest to least, the magnitudes of the loop’s induced emf for the following situations: A. The magnetic field strength increases from 0 to 1 T in 6 s. B. The magnetic field strength increases from 1 T to 4 T in 2 s. C. The magnetic field strength remains at 4 T for 1 min. D. The magnetic field strength decreases from 4 T to 3 T in 4 s. E. The magnetic field strength decreases from 3 T to 0 T in 1 s.

Problem 13CQ Figure Q25.12 shows two concentric, conducting loops. We will define a counterclockwise current (viewed from above) to be positive, a clockwise current to be negative. The graph shows the current in the outer loop as a function of time. Sketch a graph that shows the induced current in the inner loop. Explain.

Problem 14CQ Two loops of wire are stacked vertically, one above the other, as shown in Figure Q25.14. Does the upper loop have a clockwise current, a counterclockwise current, or no current at the following times? Explain your reasoning.

Problem 14P Patients undergoing an MRI occasionally report seeing flashes of light. Some practitioners assume that this results from electric stimulation of the eye by the emf induced by the rapidly changing fields of an MRI solenoid. We can do a quick calculation to see if this is a reasonable assumption. The human eyeball has a diameter of approximately 25 mm. Rapid changes in current in an MRI solenoid can produce rapid changes in field, with ?B/?t as large as 50 T/s. What emf would this induce in a loop circling the eyeball? How does this compare to the 15 mV necessary to trigger an action potential?

Problem 15CQ A loop of wire is horizontal. A bar magnet is pushed toward the loop from below, along the axis of the loop, as shown in Figure Q25.15. a. In what direction is the current in the loop? Explain. b. Is there a magnetic force on the loop? If so, in which direction? Explain. Hint: Recall that a current loop is a magnetic dipole. c. Is there a magnetic force on the magnet? If so, in which direction?

Problem 15P A 1000-turn coil of wire 2.0 cm in diameter is in a magnetic field that drops from 0.10 T to 0 T in 10 ms. The axis of the coil is parallel to the field. What is the emf of the coil?

Problem 16CQ A bar magnet is pushed toward a loop of wire, as shown in Figure Q25.16. Is there a current in the loop? If so, in which direction? If not, why not?

Problem 16P The loop in Figure P25.20 has an induced current as shown. The loop has a resistance of 0.10 ?. Is the magnetic field strength increasing or decreasing? What is the rate of change of the field, ?B/?t?

Problem 17CQ A conducting loop around a region of strong magnetic field contains two light bulbs, as shown in Figure Q25.17. The wires connecting the bulbs are ideal. The magnetic field is increasing rapidly. a. Do the bulbs glow? Why or why not? b. If they glow, which bulb is brighter? Or are they equally bright? Explain.

Problem 17P The circuit of Figure P25.21 is a square 20 cm on a side. The magnetic field increases steadily from 0 T to 0.50 T in 10 ms. What is the current in the resistor during this time?

Problem 18CQ A metal wire is resting on a U-shaped conducting rail, as shown in Figure Q25.18. The rail is fixed in position, but the wire is free to move. a. If the magnetic field is increasing in strength, which way does the wire move? b. If the magnetic field is decreasing in strength, which way does the wire move?

Problem18P A 5.0-cm-diameter loop of wire has resistance 1.2 ?. A nearby solenoid generates a uniform magnetic field along the axis of the loop that varies with time as shown in Figure P25.22. Graph the magnitude of the current in the loop over the same time interval.

Problem 19CQ Although sunlight is unpolarized, the light that reflects from smooth surfaces may be partially polarized in the direction parallel to the plane of the reflecting surface. How should the axis of the polarizers in sunglasses be oriented—vertically or horizontally— to redu

Problem 19P What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.0 mT?

Problem 20CQ Two polarizers are oriented with axes at 90°, so no light passes through the pair. Apiece of plastic is placed between the two. If the plastic is stressed, by being squeezed, light that passes through the first polarizer and the plastic now passes through the second polarizer. The dark and light lines allow the pattern of stress to be determined. What effect does the stressed plastic have on the polarization of light passing through it? With polarizing filters Without polarizing filters

Problem 20P What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 10 V/m?

Problem 21P A microwave oven operates at 2.4 GHz with an intensity inside the oven of . What are the amplitudes of the oscillating electric and magnetic fields?

Problem 21 CQ Old-fashioned roof-mounted television antennas were designed to pick up signals across a broad frequency range. Explain why these antennas had metal bars of many different lengths.

Problem 22CQ An AM radio detects the oscillating magnetic field of the radio wave with an antenna consisting of a coil of wire wrapped around a ferrite bar, as shown in Figure. Ferrite is a magnetic material that “amplifies” the magnetic field of the wave. a. Explain how the radio antenna detects the magnetic field of the radio wave. b. If a radio station is located due north of you, how must the ferrite bar be oriented for best reception? Assume that the station broadcasts with a vertical antenna like the one shown in Figure. FIGURE

Problem 22P The maximum allowed leakage of microwave radiation from a microwave oven is . If microwave radiation outside an oven has the maximum value, what is the amplitude of the oscillating electric field?

Problem 23CQ

Problem 23P A typical helium-neon laser found in supermarket checkout scanners emits 633-nm-wavelength light in a 1.0-mm-diameter beam with a power of 1.0 mW. What are the amplitudes of the oscillating electric and magnetic fields in the laser beam?

Problem 24CQ The intensity of a beam of light is increased but the light’s frequency is unchanged. As a result, which of the following (perhaps more than one) are true? Explain. A. The photons travel faster. B. Each photon has more energy. C. The photons are larger. D. There are more photons per second.

Problem 24P The magnetic field of an electromagnetic wave in a vacuum is , where x is in m and t is in s. What are the wave’s (a) wavelength, (b) frequency, and (c) electric field amplitude?

Problem 25CQ The frequency of a beam of light is increased but the light’s intensity is unchanged. As a result, which of the following (perhaps more than one) are true? Explain. A. The photons travel faster. B. Each photon has more energy. C. There are fewer photons per second. D. There are more photons per second.

Problem 25P The electric field of an electromagnetic wave in a vacuum is Ey = (20 V/m)sin((6.28 × 108)x ? 2?ft), where x is in m and t is in s. What are the wave’s (a) wavelength, (b) frequency, and (c) magnetic field amplitude?

Problem 26CQ Arc welding uses electric current to make an extremely hot electric arc that can melt metal. The arc emits ultraviolet light that can cause sunburn and eye damage if a welder is not wearing protective gear. Why does the arc give off ultraviolet light?

Problem 26P A radio receiver can detect signals with electric field amplitudes as small as 300 ?V/m. What is the intensity of the smallest detectable signal?

Problem 27MCQ A circular loop of wire has an area of . It is tilted by 45° with respect to a uniform 0.40 T magnetic field. What is the magnetic flux through the loop?

Problem 27P A 200 MW laser pulse is focused with a lens to a diameter of ‘ 2.0 ?m. a. What is the laser beam’s electric field amplitude at the focal point? b. What is the ratio of the laser beam’s electric field to the electric field that keeps the electron bound to the proton of a hydrogen atom? The radius of the electron’s orbit is 0.053 nm.

Problem 28MCQ In Figure Q25.27, a square loop is rotating in the plane of the page around an axis through its center. A uniform magnetic field is directed into the page. What is the direction of the induced current in the loop?

Problem 28P A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. Assume that the radiation is emitted uniformly in all directions. a. What is the wave’s intensity 30 km from the antenna? b. What is the electric field amplitude at this distance?

Problem 29MCQ A diamond-shaped loop of wire is pulled at a constant velocity through a region where the magnetic field is directed into the paper in the left half and is zero in the right half, as shown in Figure Q25.28. As the loop moves from left to right, which graph best represents the induced current in the loop as a function of time? Let a clockwise current be positive and a counterclockwise current be negative.

Problem 29P At what distance from a 10 W point source of electromagnetic waves is the electric field amplitude (a) 100 V/m and (b) 0.010 V/m?

Problem 30MCQ Figure Q25.29 shows a triangular loop of wire in a uniform magnetic field. If the field strength changes from 0.30 to 0.10 T in 50 ms, what is the induced emf in the loop? A. 0.08 V B. 0.12 V C. 0.16 V D. 0.24 V E. 0.36 V

Problem 30P The intensity of a polarized electromagnetic wave is . What will be the intensity after passing through a polarizing filter whose axis makes the following angles with the plane of polarization? (a) ? = 0°, (b) ? = 30°, (c) ? = 45°, (d) ? = 60°, (e) ? = 90°.

Problem 31MCQ A device called a flip coil can be used to measure the earth’s magnetic field. The coil has 100 turns and an area of . It is oriented with its plane perpendicular to the earth’s magnetic field, then flipped 180° so the field goes through the coil in the opposite direction. The earth’s magnetic field is 0.050 mT, and the coil flips over in 0.50 s. What is the average emf induced in the coil during the flip? A. 0.050 mV B. 0.10 mV C. 0.20 mV D. 1.0 mV

Problem 31P Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?

Problem 32MCQ The electromagnetic waves that carry FM radio range in frequency from 87.9 MHz to 107.9 MHz. What is the range of wavelengths of these radio waves? A. 500–750 nm B. 0.87–91.08 m C. 2.78–3.41 m D. 278–341 m E. 234–410 km

Problem 32P A 200 mW horizontally polarized laser beam passes through a polarizing filter whose axis is 25° from vertical. What is the power of the laser beam as it emerges from the filter?

Problem 33MCQ A spacecraft in orbit around the moon measures its altitude by reflecting a pulsed 10 MHz radio signal from the surface. If the spacecraft is 10 km high, what is the time between the emission of the pulse and the detection of the echo? A. 33 ns B. 67 ns C. 33 ?s D. 67 ?s

Problem 33P The polarization of a helium-neon laser can change with time. The light from a 1.5 mW laser is initially horizontally polarized; as the laser warms up, the light changes to be vertically polarized. Suppose the laser beam passes through a polarizer whose axis is 30° from horizontal. By what percent does the light intensity transmitted through the polarizer decrease as the laser warms up?

Problem 34MCQ A 6.0 mW vertically polarized laser beam passes through a polarizing filter whose axis is 75° from vertical. What is the laser-beam power after passing through the filter? A. 0.40 Mw B. 1.0 mW C. 1.6 mW D. 5.6 mW

Problem 34P What is the energy (in eV) of a photon of visible light that has a wavelength of 500 nm?

Problem 35MCQ Communication with submerged submarines via radio waves is difficult because seawater is conductive and absorbs electromagnetic waves. Penetration into the ocean is greater at longer wavelengths, so the United States has radio installations that transmit at 76 Hz for submarine communications. What is the approximate wavelength of those extremely low-frequency waves? A. 500 km B. 1000 km C. 2000 km D. 4000 km

Problem 35P What is the energy (in eV) of an x-ray photon that has a wavelength of 1.0 nm?

Problem 36MCQ How many photons are emitted during 5.0 s of operation of a red laser pointer? The device outputs 2.8 mW at a 635 nm wavelength.

Problem 36P What is the wavelength of a photon whose energy is twice that of a photon with a 600 nm wavelength?

Problem 37P One recent study has shown that x rays with a wavelength of 0.0050 nm can produce mutations in human cells. a. Calculate the energy in eV of a photon of radiation with this wavelength. b. Assuming that the bond energy holding together a water molecule is typical, use Table 25.1 to estimate how many molecular bonds could be broken with this energy.

Problem 38P Rod cells in the retina of the eye detect light using a photopigment called rhodopsin. 1.8 eV is the lowest photon energy that can trigger a response in rhodopsin. What is the maximum wavelength of electromagnetic radiation that can cause a transition? In what part of the spectrum is this?

Problem 39P What is the energy of 1 mol of photons that have a wavelength of 1.0 ?m?

Problem 40P The thermal emission of the human body has maximum intensity at a wavelength of approximately 9.5 ?m. What photon energy corresponds to this wavelength?

Problem 41P The intensity of electromagnetic radiation from the sun reaching the earth’s upper atmosphere is . Assuming an average wavelength of 680 nm for this radiation, find the number of photons per second that strike a solar panel directly facing the sun on an orbiting satellite.

Problem 42P The human eye can barely detect a star whose intensity at the earth’s surface is . If the dark-adapted eye has a pupil diameter of 7.0 mm, how many photons per second enter the eye from the star? Assume the starlight has a wavelength of 550 nm.

Problem 43P The spectrum of a glowing filament has its peak at a wavelength of 1200 nm. What is the temperature of the filament, in °C?

Problem 44P While using a dimmer switch to investigate a new type of incandescent light bulb, you notice that the light changes both its spectral characteristics and its brightness as the voltage is increased. a. If the wavelength of maximum intensity decreases from 1800 nm to 1600 nm as the bulb’s voltage is increased, by how many °C does the filament temperature increase? b. By what factor does the total radiation from the filament increase due to this temperature change?

Problem 45P The photon energies used in different types of medical x-ray imaging vary widely, depending upon the application. Single dental x rays use photons with energies of about 25 keV. The photon energy used for x-ray microtomography, a process that allows repeated imaging in single planes at varying depths within the sample, is 2.5 times greater. What are the wavelengths of the x rays used for these two purposes?

Problem 46GP A 10 cm × 10 cm square is bent at a 90° angle as shown in Figure. A uniform 0.050 T magnetic field points downward at a 45° angle. What is the magnetic flux through the loop? FIGURE

Problem 47GP What is the magnetic flux through the loop shown in Figure? FIGURE

Problem 48GP a. A circular loop antenna has a diameter of 20 cm. If the plane of the loop is perpendicular to the earth’s 50 ?T magnetic field, what is the flux through the loop? ________________ b. What is the flux if the loop is rotated by 30°?

Problem 49GP An 1.1-m-diameter MRI solenoid with a length of 2.4 m has a magnetic field of 1.5 T along its axis. If the current is turned off in a time of 1.2 s, what is the induced emf in one turn of the solenoid’s windings?

Problem 50GP A magnet and a coil are oriented as shown in Figure P25.14. The magnet is moved rapidly into the coil, held stationary in the coil for a short time, and then rapidly pulled back out of the coil. Sketch a graph showing the reading of the ammeter as a function of time. The ammeter registers a positive value when current goes into the “ +” terminal.

Problem 51GP A wire loop with an area of 0.020 m2 is in a magnetic field of 0.30 T directed at a 30° angle to the plane of the loop. If the field drops to zero in 45 ms, what is the average induced emf in the loop?

Problem 52GP A 100-turn, 2.0-cm-diameter coil is at rest in a horizontal plane. A uniform magnetic field 60° away from vertical increases from 0.50 T to 1.50 T in 0.60 s. What is the induced emf in the coil?

Problem 53GP A 25-turn, 10.0-cm-diameter coil is oriented in a vertical plane with its axis aligned east-west. A magnetic field pointing to the northeast decreases from 0.80 T to 0.20 T in 2.0 s. What is the emf induced in the coil?

Problem 54GP People immersed in strong unchanging magnetic fields occasionally report sensing a metallic taste. Some investigators suspect that motion in the constant field could produce a changing flux and a resulting emf that could stimulate nerves in the tongue. We can make a simple model to see if this is reasonable by imagining a somewhat extreme case. Suppose a patient having an MRI is immersed in a 3.0 T field along the axis of his body. He then quickly tips his head to the side, toward his right shoulder, tipping his head by 30° in the rather short time of 0.15 s. Estimate the area of the tongue; then calculate the emf that could be induced in a loop around the outside of the tongue by this motion of the head. How does this emf compare to the approximately 15 mV necessary to trigger an action potential? Does it seem reasonable to suppose that an induced emf is responsible for the noted effect?

Problem 55GP A 20 cm length of 0.32-mm-diameter nichrome wire is welded into a circular loop. The loop is placed between the poles of an electromagnet, and a field of 0.55 T is switched on in a time of 15 ms. What is the induced current in the loop?

Problem 56GP Currents induced by rapid field changes in an MRI solenoid can, in some cases, heat tissues in the body, but under normal circumstances the heating is small. We can do a quick estimate to show this. Consider the “loop” of muscle tissue shown in Figure P25.61. This might be muscle circling the bone of your arm or leg. Muscle tissue is not a great conductor, but current will pass through muscle and so we can consider this a conducting loop with a rather high resistance. Suppose the magnetic field along the axis of the loop drops from 1.6 T to 0 T in 0.30 s, as it might in an MRI solenoid. a. How much energy is dissipated in the loop? b. By how much will the temperature of the tissue increase? Assume that muscle tissue has resistivity 13 ? · m, density , and specific heat 3600 J/kg · K.

Problem 57GP A 100-turn, 8.0-cm-diameter coil is made of 0.50-mm- diameter copper wire. A magnetic field is perpendicular to the coil. At what rate must B increase to induce a 2.0 A current in the coil?

Problem 58GP The loop in Figure P25.62 is being pushed into the 0.20 T magnetic field at 50 m/s. The resistance of the loop is 0.10 ?. What are the direction and magnitude of the current in the loop?

Problem 59GP A 20-cm-long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of 10 m/s in a 0.10 T magnetic field. (See Figure P25.63.) On the opposite side, a 1.0 ? carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. a. What is the induced current in the circuit? b. How much force is needed to pull the wire at this speed? c. How much does the temperature of the carbon increase if the wire is pulled for 10 s? The specific heat of carbon is 710 J/kg · K. Neglect thermal energy transfer out of the resistor.

Problem 60GP A TMS (transcranial magnetic stimulation) device creates very rapidly changing magnetic fields. The field near a typical pulsed-field machine rises from 0 T to 2.5 T in 200 ms. Suppose a technician holds his hand near the device so that the axis of his 2.0-cm-diameter wedding band is parallel to the field. a. What emf is induced in the ring as the field changes? b. If the band is made of a gold alloy with resistivity and has a cross-section area of , what is the induced current?

Problem 61GP The 10-cm-wide, zero-resistance wire shown in Figure P25.65 is pushed toward the 2.0 ? resistor at a steady speed of 0.50 m/s. The magnetic field strength is 0.50 T. a. What is the magnitude of the pushing force? b. How much power does the pushing force supply to the wire? c. What are the direction and magnitude of the induced current? d. How much power is dissipated in the resistor?

Problem 62GP Experiments to study vision often need to track the movements of a subject’s eye. One way of doing so is to have the subject sit in a magnetic field while wearing special contact lenses that have a coil of very fine wire circling the edge. A current is induced in the coil each time the subject rotates his eye. Consider an experiment in which a 20-turn, 6.0-mm-diameter coil of wire circles the subject’s cornea while a 1.0 T magnetic field is directed as shown in Figure P25.66. The subject begins by looking straight ahead. What emf is induced in the coil if the subject shifts his gaze by 5.0° in 0.20 s?

Problem 63GP The filament in the center of a 100 W incandescent bulb emits approximately 4.0 W of visible light. If you assume that all of this light is emitted at a single wavelength, estimate the electric and magnetic field strength at the surface of the bulb.

Problem 64GP A LASIK vision correction system uses a laser that emits 10-ns-long pulses of light, each with 2.5 mJ of energy. The laser is focused to a 0.85-mm-diameter circle. (a) What is the average power of each laser pulse? (b) What is the electric field strength of the laser light at the focus point?

Problem 65GP When the Voyager 2 spacecraft passed Neptune in 1989, it was from the earth. Its radio transmitter, with which it sent back data and images, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions, a. What signal intensity was received on the earth? b. What electric field amplitude was detected? (The received signal was slightly stronger than your result because the spacecraft used a directional antenna.)

Problem 66GP A new cordless phone emits 4.0 mW at 5.8 GHz. The manufacturer claims that the phone has a range of 100 feet. If we assume that the wave spreads out evenly with no obstructions, what is the electric field strength at the base unit 100 feet from the phone?

Problem 67GP 633-nm-wavelength light from a helium-neon laser is vertically polarized. Suppose a laser beam passes through a polarizer with its axis 45° from the vertical. What is the ratio of the laser beam’s electric field strengths before and after the polarizer?

Problem 68GP In reading the instruction manual that came with your garagedoor opener, you see that the transmitter unit in your car produces a 250 mW signal and that the receiver unit is supposed to respond to a radio wave of the correct frequency if the electric field amplitude exceeds 0.10 V/m. You wonder if this is really true. To find out, you put fresh batteries in the transmitter and start walking away from your garage while opening and closing the door. Your garage door finally fails to respond when you’re 42 m away. Are the manufacturer’s claims true?

Problem 69GP Unpolarized light passes through a vertical polarizing filter, emerging with an intensity . The light then passes through a horizontal filter, which blocks all of the light; the intensity transmitted through the pair of filters is zero. Suppose a third polarizer with axis 45° from vertical is inserted between the first two. What is the transmitted intensity now?

Problem 70GP a. What is the wavelength of a gamma-ray photon with energy 1.0 × 10?13 J? b. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of this one gamma-ray photon?

Problem 71GP Gamma rays with the very high energy of 2.0 × 1013 eV are occasionally observed from distant astrophysical sources. What are the wavelength and frequency corresponding to this photon energy?

Problem 72GP A 1000 kHz AM radio station broadcasts with a power of 20 kW. How many photons does the transmitting antenna emit each second?

Problem 73GP Fireflies emit flashes of light to communicate, directly converting chemical energy into the energy of visible-light photons. A firefly emits a 0.15-s-long pulse of light with an average wavelength of 590 nm. During the flash, the emitted power is 40 ?W. a. What is the energy of one light photon having the average wavelength? b. Assume that all photons have the average wavelength. How many photons does the firefly emit during each flash?

Problem 74GP The human body has a surface area of approximately , a surface temperature of approximately 30°C, and a typical emissivity at infrared wavelengths of e = 0.97. If we make the approximation that all photons are emitted at the wavelength of peak intensity, how many photons per second does the body emit?

Problem 75GP For radio and microwaves, the depth of penetration into the human body is approximately proportional to . If 27 MHz radio waves penetrate to a depth of 14 cm, estimate the depth of penetration of 2.4 GHz microwaves.

Problem 76PP The Metal Detector Metal detectors use induced currents to sense the presence of any metal—not just magnetic materials such as iron. A metal detector, shown in Figure P25.78, consists of two coils: a transmitter coil and a receiver coil. A high-frequency oscillating current in the transmitter coil generates an oscillating magnetic field along the axis and a changing flux through the receiver coil. Consequently, there is an oscillating induced current in the receiver coil. If a piece of metal is placed between the transmitter and the receiver, the oscillating magnetic field in the metal induces eddy currents in a plane parallel to the transmitter and receiver coils. The receiver coil then responds to the superposition of the transmitter’s magnetic field and the magnetic field of the eddy currents. Because the eddy currents attempt to prevent the flux from changing, in accordance with Lenz’s law, the net field at the receiver decreases when a piece of metal is inserted between the coils. Electronic circuits detect the current decrease in the receiver coil and set off an alarm. The metal detector will not detect insulators because A. Insulators block magnetic fields. B. No eddy current can be produced in an insulator. C. No emf can be produced in an insulator. D. An insulator will increase the field at the receiver.

Problem 77PP The Metal Detector Metal detectors use induced currents to sense the presence of any metal—not just magnetic materials such as iron. A metal detector, shown in Figure P25.78, consists of two coils: a transmitter coil and a receiver coil. A high-frequency oscillating current in the transmitter coil generates an oscillating magnetic field along the axis and a changing flux through the receiver coil. Consequently, there is an oscillating induced current in the receiver coil. If a piece of metal is placed between the transmitter and the receiver, the oscillating magnetic field in the metal induces eddy currents in a plane parallel to the transmitter and receiver coils. The receiver coil then responds to the superposition of the transmitter’s magnetic field and the magnetic field of the eddy currents. Because the eddy currents attempt to prevent the flux from changing, in accordance with Lenz’s law, the net field at the receiver decreases when a piece of metal is inserted between the coils. Electronic circuits detect the current decrease in the receiver coil and set off an alarm. A metal detector can detect the presence of metal screws used to repair a broken bone inside the body. This tells us that A. The screws are made of magnetic materials. B. The tissues of the body are conducting. C. The magnetic fields of the device can penetrate the tissues of the body. D. The screws must be perfectly aligned with the axis of the device.

Problem 79PP The Metal Detector Metal detectors use induced currents to sense the presence of any metal—not just magnetic materials such as iron. A metal detector, shown in Figure P25.78, consists of two coils: a transmitter coil and a receiver coil. A high-frequency oscillating current in the transmitter coil generates an oscillating magnetic field along the axis and a changing flux through the receiver coil. Consequently, there is an oscillating induced current in the receiver coil. If a piece of metal is placed between the transmitter and the receiver, the oscillating magnetic field in the metal induces eddy currents in a plane parallel to the transmitter and receiver coils. The receiver coil then responds to the superposition of the transmitter’s magnetic field and the magnetic field of the eddy currents. Because the eddy currents attempt to prevent the flux from changing, in accordance with Lenz’s law, the net field at the receiver decreases when a piece of metal is inserted between the coils. Electronic circuits detect the current decrease in the receiver coil and set off an alarm. Which of the following changes would not produce a larger eddy current in the metal? A. Increasing the frequency of the oscillating current in the transmitter coil B. Increasing the magnitude of the oscillating current in the transmitter coil C. Increasing the resistivity of the metal D. Decreasing the distance between the metal and the transmitter

Problem 78PP Suppose the magnetic field from the transmitter coil in Figure points toward the receiver coil and is increasing with time. As viewed along this axis, the induced currents are FIGURE A. Clockwise in the metal, clockwise in the receiver coil B. Clockwise in the metal, counterclockwise in the receiver coil C. Counterclockwise in the metal, clockwise in the receiver coil D. Counterclockwise in the metal, counterclockwise in the receiver coil