Figure Q25. 13 shows conducting loops next to each other.

The world's strongest magnet can produce a steady fie ld of 45 T . If a circular wire loop of radius I 0 cm were held in this magnetic fi eld, what cun-ent would be induced in the loop?

The rapid vibrat ion accompany~n g 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 techn ique works.

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, deten-nine if the induced cun-ent is clockwise, counterclockwise, or zero.

Figure Q25.4 shows four different loops in a magnetic fi e ld. The numbers indicate the lengths of the s ides and the strength of the fi eld. Rank in order the magnetic fluxes cl>1 through cl>4 , from the largest to the smallest. Some may be equal. Explain.

Figure Q25.5 shows four different circular loops that are perpendicular to the page. The radius o f loops 3 and 4 is twice that of loops I and 2. The magnetic field is the same for each. Rank in order the ma<metic flu xes cl> throu"h cl> from the lar"est to the smallest. Some may be equal. Explain.

circular loop rotates at constant speed about an axle through the center of the loop. Figure Q25.6 shows an edge view and defines lhe angle <f>, which increases f,rom 0 to 360 as lhe loop rotates. a. At what angle or angles is the magnetic flux a maximum? b. At what angle or angles is the magmagnetic flux a mininum? c. At what angle or angles is the magnetic flux changing most rapidly?

The power lines that run through your neighborhood can-y alrernaring currenr.~ that reverse direction 120 times pe r second. As the cun-ent changes, so does the magnetic t'ield around a line . Suppose you wanted to put a loop of wire up near the power line to extract power by " tapping" the magoetic fi eld. 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.)

The magnetic flux passing through a coil of wi re varies as shown in Figure Q25.8. During which time interval(s) will an induced c urrent be present in the coil? Explain.

There is a counterclockwise induced current in the conducting loop shown in Figure Q25.9. ls the magnetic fi eld inside the loop increasing in strength, decreasing in strength, or steady?

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

The conducting loop in Figure Q25. I I LJ is moving into the region between the magnetic poles shown. .....-a. L~ lhe induced cun-ent (viewed from above) clockwise or counterclockwise? b. Is there an attractive magnetic force that te nds to pull the loop in, like a magnet pulls on a paper clip Or do

Figure Q25. l 2 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 func tion of time. Sketch a graph that shows the induced current in the inner loop. Explain.

Figure Q25. 13 shows conducting loops next to each other. We will define a counterclockwise current (viewed from above) to be positi ve, a clockwise current to be negati ve. The graph shows the current in the left loop as a function of time. Sketch a graph that shows the induced current in the right loop. Explai.n.

Two loops of wire are stacked vertically, one above the other, as shown in Figure Q25. l 4. Does the upper loop have a clockwise current, a counterclockwise current, or no c urrent at the following times? Explain your reasoning. a . Before the switch is closed b. Immediately after the switch is closed c. Long after the switch is closed d. Immediately after the switch is reopened

A loop of wire is horizontal. A barmagnet is pushed toward the loop from below, along the axis of the loop, as shown in Figure Q25. l 5. 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? Explai n. Hint: Recall that a c urrent loop is a magnetic dipole. c. ls there a magnetic force on the magnet? lf so, in which direction?

A bar magnet is pushed toward a loop of wire, as shown in Figure Q25. I 6. Is there a current in the loop? If so, in which direction? lf not, why not?

A conducting loop around a region of strong magnetic field contains two light bulbs, as shown in Figure Q25. I 7. The wires connecting the bulbs are ideal. The magnetic field is increasi ng rapidly. a. Do the bulbs glow? Why or why not? b. If they glow, which bulb is brighter? Or are they equally bright? Explain.

A metal wire is res ting 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. Tf the magnetic field is decreasi ng in strength, which way does the wire move?

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 hori zontally- to reduce the glare from a horizontal surface such as a road or a lake?

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 d ifferent lengths.

An AM radio detects the osci llating magnetic field of the radio wave with an antenna consisting of a coil of wire wrapped around a ferrite bar, a s shown in Figure Q25.2 I. Ferrite is a magnetic material that "amplifies" the magnetic field of the wave. The radio antenna broadcasts waves with the electric field vertical, the magnetic field horizontal. If a radio antenna is located due north of you, how must the ferrite bar be oriented for best reception?

Three laser beams have wave lengths A1 = 400 nm, A2 = 600 nm, and A3 = 800 nm. The power of each laser beam is I W. a. Rank in order, from largest to smalles t, the photon energies 1, 2, and 3 in these three laser beams. Explain. b. Rank in order, from largest to smallest, the number of photons per second N1, N2 , and N3 delivered by the three laser beams. Explain.

The intensity of a beam of light is increased but the light's fre quency 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.

The frequency of a beam of light is increased but the light's intensity is unchanged. As a result, which of the fo llowing (pe rhaps more than one) are tme? Explain. A. The photons travel faster. B. Each photon has more energy. C. IJiere are fewer photons per second. D. There are more photons per second.

Arc welding uses electric current to make an extreme ly 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?

A circular loop of wire has an area of 0.30 m2. It is tilted by 45 with respect to a uniform 0.40 T magnetic field. What is the magnetic flux through the loop? A. 0.085 T m2 B. 0. 12 T m2 C. 0.38 T m2 D. 0.75 Tm2 E. 1.3 T m2

In Figure Q25.27, a square loop is x rotating in the plane of the page around an x axis through its center. A uniform mag- netic field is directed into the page. What x is the direction of the induced current in the loop? A. Clockwise. B. Counterclockwise. C. There is no induced current.

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 be st repre sents the induced current in the loop as a fu nction of time? Let a clockwise cutTent be positive and a counterclockwise current be negative.

Figure Q25.29 shows a triangular loop of wire in a unifonn 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. 0.12V c. 0. 16 v D. 0.24 V E. 0.36 V

A device called a flip coil can be used to measure the earth's magnetic field. The coil has I 00 turns and an area of 0.0 I 0 m2 ft 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 fi eld 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 C. 0.20 mV B. O.IO mV D. 1.0 mV

The electromagnetic waves that c arry FM radio range in frequency from 87.9 MHz to 107.9 MHz. What is the range of wavelengths of these radio waves? A. 500-150 nm B. 0.87- 9 1.08 m C. 2.78- 3.41 m D. 278- 341 m E. 234-410 km

The beam from a laser is focused with a lens, reducing the area of the beam by a factor of 2. By what factor does the amplitude of the electric field increase? A. The amplitude does not c hange. B. The amplitude increases by a factor of V2. C. The amplitude increases by a factor of 2. D. The amplitude increases by a factor of 2V2. E. The amplitude increases by a factor of 4 .

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 I 0 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

A 6.0 mW vertically polarized laser beam passes thro ugh a polarizing fil ter whose axis is 75 from ve rtical. What is the laser-beam power after passing through the fi lter? A. 0.40 mW B. 1.0 mW C. 1.6 mW D. 5.6 mW

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. IOOO km C. 2000 km D. 4000 km

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. A. 4.5 x 1010 c. 4.5 x 10 15 B. 4.5 x 10 11 D. 4.5 x 10 16

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 fi lter?

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 fil ter?

The polarizat ion 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 po)arized. 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?

What is the energy (in e V) of a pboton of visible light that has a wavelength of 500 nm?

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

What is the wavele ngth of a photon whose e nergy is twice that of a photon with a 600 nm wavelength?

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.

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? Tn what part of the spectrum is this?

The thermal emission of the human body has maximum intensi ty at a wavelength of approximately 9.5 m . What photon energy corresponds to this wavelength?

Extremely high-energy photons of 2.0 X 10 13 eV are occasionally observed from distant astronomical sources. What are the corresponding wavelength and frequency?

The intensity of electromagnetic radiation from the sun reaching the earth's upper atmosphere is 1.37 kW/m2. Assuming an average wavelength of 680 nm for this radiation, find the number of photons per second that strike a 1.00 m2 solar panel directly fac ing the sun on an orbiting satellite.

A 193-nm-wavelength UV laser for eye surgery emits a 0.500 mJ pulse. How many photons does the light pulse contain?

The human eye can barely detect a star whose intensity at the earth's surface is 1.6 X 10-11 W/m2. 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.

A particular species of copepod, a small marine crustacean, BIO emits a flash of light consisting of 1.4 x I 010 photons at a wavelength of 490 nm. The flash lasts for 2.4 s. What is the power of the flash?

The spectrum of a glowing fi lament has its peak at a wavelength of 1200 nm. What is the temperature of the filament, in C?

Our sun's 5800 K surface temperature gives a peak wavelength in the middle of the visible spectrum. What is the mini mum surface temperature for a star whose emission peaks at some wavelength less than 400 nm- that is, in the ultraviolet?

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 fac tor does the total radiation from the filament increase due to this temperature change?

The star Sirius is much hotter than the sun, with a peak wavelength of 290 nm compared to the sun's 500 nm. It is also larger, with a diameter 1.7 times that of the sun. By what factor does the energy emitted by Sirius exceed that of the sun?

T he 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?

A python can detect thermal radiation with intensity greater than 0.60 W/m2 A typical human body has a surface area of 1.8 m2 , a su1face temperature of 30C, and an emissivity e = 0.97 at infrared wavelengths. What is the maximum distance from which a python can detect your presence? You can model the human body as a poi nt source of cadiation.

lf astronomers look toward any point in outer space, they see radiation that matches the emission spectrum of an object at 2.7 K, a remnant of the Big Bang. What is the peak wavelength of this radiation? What palt of the electromagnetic spectrum is it in?

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

A 25-turn, I 0.0-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 Tin 2.0 s. What is the emf induced in the coil?

People immersed in strong unchanging magnetic fi elds occasionally report sensing a metallic taste. Some investigators suspect that motion in the constant field could produce a changing flux and a resulti ng 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 outs ide 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?

Currents induced by rapid field changes in an MRI sole noid can, in some cases, heat ti ssues in the body, but under normal circumstances the heating is small. We can do a quick estimate to show th is. Consider the "loop" of muscle tissue shown in Figure P25.6 I. This might be muscle circ ling the bone of your arm or leg. Muscle tissue is not a great conductor, but CUITent 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 Tin 0.30 s, as il 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 fl m, densi ty I. I x 103 kglm3 , and specific heat 3600 Jlkg K.

The loop in Figure P25.62 is being pushed into the 0.20 T magnetic field at 50 mis. The resistance of the loop is 0. 10 n. What are the direction and magnitude of the current in the loop?

A 20-cm-long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of I 0 mis in a 0.10 T magnetic field. (See Figure P25.63.) On the opposite side, a 1.0 n carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50 mg. a. What is the induced cun-ent 10 mis 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 7 10 J/kg K. Neglect then-nal energy transfer out of the resistor.

A TMS (transcranial magnetic stimulation) device c reates very rapidly changi ng magnetic field s. The field near a typical pul sed-field machine rises from 0 T to 2.5 Tin 200 , s. Suppose a technician holds his hand near the device so that the ax is 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 6.2 X 10- 8 n m and has a cross-section area of 4.0 mm2, what is the induced cun-en l?

The JO-cm-wide, zero-resistance wire shown in Figure P25.65 is pushed toward the 2.0 n resistor at a steady speed of 0.50 mis. 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?

Experiments to study vision often need to track the move ments 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-tum, 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?

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 INT 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?

When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5 x 109 km from the earth. Tts 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 eatth? b. What electric fie ld amplitude was detected? (The received signal was slightly stronger than your result because the spacecraft used a directional antenna.)

A new cordless phone emits 4.0 mW at 5.8 GHz. The manufacturer claims that the phone has a range of I 00 feet. If we assume that the wave spreads out evenly with no obstructions, what is the electric field strength at the base unit I 00 feet from the phone?

In reading the instruction manual that came with your garagedoor opener, you see that tbe uansmitter unit in your car produces a 250 mW signal and that the receiver unit is supposed to respond to a radio wave of the con-ect frequency if the electric field amplitude exceeds 0.10 Vim. 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?

Unpolarized light passes through a vettical polarizing filter, emerging with an intensity !0. 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?

A light-emitting diode (LED) connected to a 3.0 V power supply INT emits 440 nm blue light. The current in the LED is I 0 mA, and the LED is 60% efficient at conve1ting electric power input into light power output. How many photons per second does the LED emit?

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

The human body has a surface area of approximately 1.8 m2, a surface temperature of approximately 30C, 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?

What is the wavelength of 27 MHz radio waves? A. 11 m B. 9.0 m C. 0.0 11 m D. 0.009 m

If the frequency of the radio waves is increased, the depth of penetration A. Increases. B. Does not c hange. C. Dec reases.

For 27 MHz radio waves, the wave intensity has been reduced by a factor of 3 at a depth of approximately 15 cm. At this point in the tissue, the electric field amplitude has decreased by a factor of A. 9 B. 3\/3 C. 3 D. \/3

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 fie ld at the receiver.

A metal detector can detect the presence of metal screws used to repair a bro ken 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.

Which of the following changes would not produce a larger eddy current in the metal? A. Increasi ng the frequency of the osci llating c urrent in the transmitter coil B. Increasing the magnitude of the oscillating current in the transm itter coil C. Increasing the resistivity of the metal D. Decreasing the distance between the metal and the transmitter