Essential University Physics, 3e (Wolfson) Chapter 27 Electromagnetic Induction
2 7. 1 Co nc e pt ua lQue s t i o ns 1) The three loops of wire shown in the figure are all subject to the same uniform magnetic field that does not vary with time. Loop 1 oscillates back and forth as the bob in a pendulum, loop 2 rotates about a vertical ais, and loop ! oscillates up and down at the end of a spring. "hich loop, or loops, will have an emf induced in them#
$) loop 1 only %) loop 2 only &) loop ! only ') loops 1 and 2 () loops 2 and ! $nswer % *ar 1
2) $ large magnetic flu change through a coil must induce a greater emf in the coil than a small flu change. $) True %) +alse $nswer % *ar 1
!) $ circular loop of wire lies in the plane of the paper. $n increasing magnetic field points out of the paper. "hat is the direction of the induced current in the loop# $) counterclockwise then clockwise %) clockwise then counterclockwise c ounterclockwise &) clockwise ') counterclockwise () There is no current induced in the loop. $nswer & *ar 1
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) $ coil lies flat on a tabletop in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. "hen viewed from above, what is the direction of the induced current in this coil as the field fades# $) counterclockwise then clockwise %) clockwise then counterclockwise c ounterclockwise &) clockwise ') counterclockwise () There is no current induced in the coil. $nswer ' *ar 1
3) The long straight wire in the figure carries a current I current I that that is decreasing with time at a constant rate. The circular loops $, %, and & all lie in a plane containing the wire. The induced emf in each of the loops $, %, and & is such that
$) no emf is induced in any of the loops. %) a counterclockwise emf is induced in all the loops. &) loop $ has a clockwise emf, loop % has no induced emf, and loop & has a counterclockwise emf. ') loop $ has a counterclockwise emf, loop % has no induced emf, and loop & has a clockwise emf. () loop $ has a counterclockwise emf, loops % and & have clockwise emfs. $nswer ' *ar 1
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/) The figure shows a bar magnet moving vertically upward toward a hori4ontal coil. The poles of the bar magnets are labeled 5 and 6. $s the bar magnet approaches the coil it induces an electric current in the direction indicated on the figure 7counterclockwise as viewed from above). "hat are the correct polarities of the magnet#
$) 5 is a south pole, 6 is a north pole. %) 5 is a north pole, 6 is a south pole. &) %oth 5 and 6 are north poles. ') %oth 5 and 6 are south poles. () The polarities of the magnet cannot be determined from the information given. $nswer $ *ar 1
8) $ closed, circular loop has a counterclockwise current flowing through it as viewed by a person on the right, as shown in the figure. f a second closed circular loop with the same radius approaches this loop with constant velocity along a common ais as shown, in what direction will a current flow in the approaching loop as viewed by the person on the right#
$) clockwise %) counterclockwise &) 9o current will be induced because the velocity of approach is constant. $nswer $ *ar 1
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:) $ circular metal ring is situated above a long straight wire, as shown in the figure. The straight wire has a current flowing to the right, and the current is increasing in time at a constant rate. "hich statement is true#
$) There is an induced current in the metal ring, flowing in a clockwise direction. %) There is an induced current in the metal ring, flowing in a counterclockwise direction. &) There is no induced current in the metal ring because the current in the wire is changing at a constant rate. $nswer $ *ar 1
;) n the figure, a straight wire carries a steady cu rrent I perpendicular to the plane of the page. $ bar is in contact with a pair of circular rails, and rotates about the straight wire. The direction of the induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer & *ar 1
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1) n the figure, the inner loop carries a clockwise current I that is increasing. The resistor R is in the outer loop and both loops are in the same plane. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer $ *ar 1
11) n the figure, a bar magnet moves away from the solenoid. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer $ *ar 1
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12) n the figure, a copper bar is in contact with a pair of parallel metal rails and is in motion with velocity ν. $ uniform magnetic field is present pointing downward, as shown. The bar, the rails, and the resistor R are all in the same plane. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer & *ar 1
1!) n the figure, two parallel wires carry currents of magnitude I in opposite directions. $ rectangular loop is midway between the wires. The current I is decreasing with time. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer $ *ar 1
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1) $ bar magnet is held vertically with its upper end a little bit below the center of a hori4ontal metal ring. The upper end of the magnet is its north pole, as shown in the figure. The bar magnet is now dropped. $n observer views the ring from above its center. To this observer, how will the induced current in the ring behave as the magnet falls#
$) The current will flow clockwise and be increasing. %) The current will flow clockwise and be decreasing. &) The current will flow counterclockwise and be increasing. ') The current will flow counterclockwise and be decreasing. () The induced current will be 4ero. $nswer ' *ar 1
13) n the figure, two solenoids are side by side. The switch S , initially open, is closed. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer % *ar 1
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1/) n the figure, two solenoids are approaching each other with speed v as shown. The induced current through the resistor R is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer $ *ar 1
18) n the figure, a straight wire carries a current I . The wire passes through the center of a toroidal coil. f the current in the wire is
$) from a to b. %) from b to a. &) There is no induced current through the resistor. $nswer % *ar 1
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1:) n the figure, a &shaped conductor is in a uniform magnetic field B, which is increasing. The polarity of the induced emf in terminals X and Y is
$) X and Y are at the same potential. %) X is positive and Y is negative. &) X is negative and Y is positive. $nswer & *ar 1
1;) The figure shows three metal coils labeled $, %, and & heading towards a region where a uniform static magnetic field eists. The coils move with the same constant velocity and all have the same resistance. Their relative si4es are indicated by the background grid. $s they enter the magnetic field the coils will have an induced electric current in them. +or which coil will the current be the greatest#
$) $ %) % &) & ') The current is the same in all three cases since all the coils move with the same velocity. () There is no induced current in any of the coils since they move at constant velocity. $nswer & *ar 1
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2) $ capacitor is charging in a simple RC circuit with a dc battery. "hich one of the following statements about this capacitor is accurate# $) There is a magnetic field between the ca pacitor plates because charge travels between the plates by jumping from one plate to the other. %) There is no magnetic field between the capacitor plates because no charge travels between the plates. &) There is a magnetic field between the cap acitor plates, even though no charge travels between them, because the magnetic flu between the plates is changing. ') There is a magnetic field between the ca pacitor plates, even though no charge travels between them, because the electric flu between the plates is changing. () The magnetic field between the capacitor plates is increasing with time because the charge on the plates is increasing. $nswer ' *ar 1
21) $ resistor and an ideal inductor are connected in series to an ideal battery having a constant terminal voltage V . $t the moment contact is made with the battery, 7a) the voltage across the resistor is $) V . %) V =e. &) V =2. ') 4ero. 7b) the voltage across the inductor is $) V . %) V =e. &) V =2. ') 4ero. $nswer 7a) ' 7b) $ *ar 1
22) "hich of the following statements about inductors are correct# There may b e more than one correct choice. $) "hen it is connected in a circuit, an inductor always resists having current flow through it. %) nductors store energy by building up charge. &) "hen an inductor and a resistor are connected in series with a '& battery, the current in the circuit is reduced to 4ero in one time constant. ') $n inductor always resists any change in the current through it. () "hen an inductor and a resistor are connected in series with a '& battery, the current in the circuit is 4ero after a very long time. $nswer ' *ar 1
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2 7 . 2 Pr o bl e ms 1) $ circular loop of radius .1 m is rotating in a uniform eternal magnetic field of .2 T. +ind the magnetic flu through the loop due to the eternal field when the plane of the loop and the magnetic field vector are 7a) parallel. 7b) perpendicular. 7c) at an angle of !> with each other. $nswer 7a) 4ero 7b) /.! ? 1! T @ m2 7c) !.1 ? 1! T @ m2 *ar 1
2) $ 2.m long conducting wire is formed into a s
!) $ 2loop coil of cross sectional area :.3 cm2 lies in the plane of the page. $n eternal magnetic field of ./ T is directed out of the p lane of the page. The eternal field decreases to .2 T in 12 milliseconds. 7a) "hat is the magnitude of the change in the eternal magnetic flu enclosed by the coil# 7b) "hat is the magnitude of the average voltage induced in the coil as the eternal flu is changing# 7c) f the coil has a resistance of . ohms, what is the magnitude of the average current in the coil# $nswer 7a) . ? 1! T @ m2 7b) .38 * 7c) .1 $ *ar 1
) $ tenloop coil having an area of .2! m2 and a very large resistance is in a .8T uniform magnetic field oriented so that the maimum flu go es through the coil. The coil is then rotated so that the flu through it goes to 4ero in .! s. "hat is the magnitude of the average emf induced in the coil during the .! s# $) .!2 * %) . * &) .!2 * ') .!2 * () 1. * $nswer ' *ar 1
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3) $ uniform magnetic field is applied perpendicular to the plane of a /turn circular coil with a radius of /. cm and a resistance of ./ A. f the magnetic field increases u niformly from .2 T to 1.: T in .2 s, what is the magnitude of the emf induced in the coil# $) 8.2 * %) 3. * &) ;.2 * ') 12 * () 1/ * $nswer % *ar 1
/) $ loop of radius r B !. cm is placed parallel to the xyplane in a uniform magnetic field
B
.83 T . The resistance of the loop is 1: A. Ctarting at t B , the magnitude of the field decreases uniformly to 4ero in .13 seconds. "hat is the magnitude of the electric current produced in the loop during that time# $) .8; m$ %) !.; m$ &) 1.8 m$ ') 2.1 m$ () .2 m$ $nswer $ *ar 1
8) $ circular coil of radius 3. cm and resistance .2 A is placed in a uniform magnetic field perpendicular to the plane of the coil. The magnitude of the field changes with time according to B = .3e2t T. "hat is the magnitude of the current induced in the coil at the time t B 2. s# $) 1.! m$ %) ;.2 m$ &) 8.3 m$ ') .2 m$ () 2./ m$ $nswer ( *ar 1
:) $ coil of 1/ turns and area .2 m2 is placed with its ais parallel to a magnetic field of initial magnitude . T. The magnetic field changes uniformly from . T in the D x direction to . T in the x direction in 2. s. f the resistance of the coil is 1/ A, at what rate is power generated in the coil# $) 3. " %) 1 " &) 13 " ') 2 " () 23 " $nswer % *ar 1
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;) $ closed loop conductor that forms a circle with a radius of is located in a uniform but changing magnetic field. f the maimum emf induced in the loop is what is the maimum rate at which the magnetic field strength is chang ing if the magnetic field is oriented perpendicular to the plane in which the loop lies# $) . T=s %) 2.3 T=s &) .: T=s ') 3. T=s $nswer $ *ar ;
1) $s shown in the figure, a wire and a 1A resistor are used to form a circuit in the shape of a s
$) /! m$, from b to a. %) !: m$, from b to a. &) /! m$, from a to b. ') !: m$, from a to b. () ;3 m$, from a to b. $nswer $ *ar 3D
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11) $ conducting bar moves along frictionless conducting rails connected to a .A resistor as shown in the figure. The length of the bar is 1./ m and a uniform magnetic field of 2.2 T is applied perpendicular to the paper pointing outward, as shown. 7a) "hat is the applied force re
$nswer 7a) 1:./ 9
7b) 112 "
*ar 1
12) $ conducting bar slides without friction on two parallel hori4ontal rails that are 3 cm apart and connected by a wire at one end. The resistance of the bar and the rails is constant and e
1!) $ 3cm wire placed in an eastwest direction is moved hori4ontally to the north with a speed of 2. m=s. The hori4ontal component of the earthEs magnetic field at that location is 23 FT toward the north and the vertical component is 3FT downward. "hat is the emf induced between the ends of the wire# $) 1 G* %) 2 G* &) ! G* ') G* () 3 G* $nswer ( *ar 1
1) +or a long ideal solenoid having a circular crosssection, the magnetic field strength within 1 &opyright - 21/ 0earson (ducation, nc.
the solenoid is given by the e
13) The coil in a /H4 ac generator has 123 turns, each having an area of !. ? 12 m2 and is rotated in a uniform .12T magnetic field. "hat is the peak output voltage of this generator# $) 18 * %) 12 * &) 2 * ') 11 * () 22 * $nswer $ *ar 1
1/) Cuppose that you wish to construct a simple ac generator having an output of 12 * maimum when rotated at / H4. $ uniform magnetic field of .3 T is available. f the area of the rotating coil is 1 cm2, how many turns do you need# $) : %) 1/ &) !2 ') / () 12: $nswer ' *ar 1
18) 6ou are designing a generator to have a maimum emf of :. *. f the generator coil has 2 turns and a crosssectional area of .! m2, what should be the fre
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1:) $ rectangular coil having N turns and measuring 13 cm by 23 cm is rotating in a uniform 1./ T magnetic field with a fre
1;) "ire is wound on a s angle with the hori4ontal, as shown. $t that instant, what is the magnitude of the emf induced in the coil#
$) 1! * %) 2! * &) 2.1 * ') !./ * () 2/ * $nswer $ *ar 1
2) "hat is the selfinductance of a solenoid !. c m long having 1 turns of wire and a cross sectional area of 1. ? 1 m2# 7 μ B π ? 18 T @ m=$) $) .1; nH %) .1; pH &) .1; GH ') .1; mH () .1; H $nswer & *ar 1
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21) $t what rate would the current in a 1mH inductor have to change to induce an emf of 1 * in the inductor# $) 1 $=s %) 1 $=s &) 1 $=s ') 1, $=s () 1 $=s $nswer ' *ar 1
22) $n inductor has a current I 7t ) B 7.3 $) cosI7283
)t J flowing through it. f the maimum
emf across the inductor is e
2!) n the figure, the current in a solenoid having no appreciable resistance is flowing from b to a and is decreasing at a rate of ;./ $=s. The selfinduced emf in the solenoid is found to be :. *.
7a) "hat is the selfinductance of the solenoid# 7b) "hich point, a or b is at higher potential# $nswer 7a) .:: H 7b) point a *ar 3D
2) $n insulated wire of diameter 1. mm and negligible resistance is wrapped tightly around a cylindrical core of radius 3. cm and length ! cm to build a solenoid. "hat is the energy stored in this solenoid when a current I B .2 $ flows through it# 7 μ B π ? 18 T @ m=$) $) 1.2 ? 1 K %) ;./ ? 1 K &) .: ? 1 K ') 2. ? 1 K () 3.; ? 13 K $nswer ( *ar 1
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23) $ solenoid of length .8 m having a circular crosssection of radius 3. cm stores /. GK of energy when a .$ current runs through it. "hat is the winding density of the solenoid# 7 μ B π ? 18 T @ m=$) $) :/3 turns=m %) 82 turns=m &) 1: turns=m ') 1 turns=m () !28 turns=m $nswer ' *ar 1
2/) $t a certain instant the current flowing through a 3.H inductor is !. $. f the energy in the inductor at this instant is increasing at a rate of !. K=s, how fast is the current changing# $) .2 $=s %) . $=s &) .1 $=s ') .: $=s $nswer $ *ar 1
28) How much energy is stored in a room !. m by . m by 2. m due to the earthEs magnetic field with a strength of 3. ? 1 3 T# 7 μ B π ? 18 T @ m=$) $) 38 mK. %) 2; mK. &) 1 mK. ') 1 mK. () 383 mK. $nswer % *ar 1
2:) "hat is the energy density in the magnetic field 23 cm from a long straight wire carrying a current of 12 $# 7 μ B π ? 18 T @ m=$) $) 8.! ? 13 K=m! %) !.8 ? 13 K=m! &) !./ ? 1 K=m! ') 1.2 ? 1 K=m! () The density cannot be determined without kn owing the volume. $nswer % *ar 1
2;) $ series circuit consists of a .33H inductor with internal resistance of :. A connected in series with a .A resistor, an open switch, and an ideal 12* battery. 7a) "hen the switch is closed, what is the initial current through the .A resistor# 7b) "hat is the current through the .A resistor a very long time after the switch is closed# $nswer 7a) . $ 7b) 1. $ *ar 1
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!) $ 3mH ideal inductor is connected in series with a /A resistor through an ideal 13* '& power supply and an open switch. f the switch is closed at time t B s, what is the current 8. ms later# $) 23 m$ %) /3 m$ &) 33 m$ ') 2: m$ () :3 m$ $nswer $ *ar 3
!1) $ series LR circuit consists of a 2.H inductor with negligible internal resistance, a 1 ohm resistor, an open switch, and a ;.* ideal power source. $fter the switch is closed, what is the maimum power delivered by the power supply# $) . " %) :1 " &) .; " ') :.1 " () .:1 " $nswer ( *ar 1
!2) "hat resistance should be added in series with a !.H inductor to complete an LR circuit with a time constant of # $) .83 k A %) 12 A &) .83 A ') 2.3 A $nswer $ *ar 2:
!!) $ series LR circuit contains an emf source of having no internal resistance, a resistor, a inductor having no appreciable resistance, and a switch. f the emf across the inductor is of its maimum value after the switch is closed, what is the resistance of the resistor# $) 1 A %) 1.; A &) 1.3 A ') 3. A $nswer % *ar 3D
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!) $n LR circuit contains an ideal /* battery, a 2H inductor having no resistance, a 2A resistor, and a switch S , all in series. nitially, the switch is open and has been open for a very long time. $t time t B s, the switch is suddenly closed. How long after closing the switch will the potential difference across the inductor be 2 *# $) 1./ s %) 1. s &) 1.: s ') 1.; s () 2.1 s $nswer $ *ar 1
!3) $n LR circuit contains an ideal /* battery, a 31H inductor having no resistance, a 21A resistor, and a switch S , all in series. nitially, the switch is open and has been open for a very long time. $t time t B s, the switch is suddenly closed. "hen the voltage across the resistor is e
!/) +or the circuit shown in the figure, the inductors have no appreciable resistance and the switch has been open for a very long time.
7a) The instant after closing the switch, what is the current through the /.A resistor# 7b) The instant after closing the switch, what is the potential difference across the 13.mH inductor# 7c) $fter the switch has been closed and left closed for a very long time, what is the potential drop across the /.A resistor# $nswer 7a) 1.! $ 7b) :3.8 * 7c) . * *ar 1
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!8) +or the circuit shown in the figure, the switch has been open for a very long time.
7a) "hat is the potential drop across the 13.mH inductor just after closing the switch# 7b) "hat is the potential drop across the 8.G+ capacitor after the switch has been closed for a very long time# $nswer 7a) 13. * 7b) 1!! * *ar 1
!:) $n ideal solenoid is 1:.3 cm long, has a circular crosssection 2.2 cm in diameter, and contains 33 e
!;) &onsider the circuit shown in the figure. The battery has emf B 23 volts and negligible internal resistance. The inductance is and the resistances are R1 B 12 A and R2 B ;. A. nitially the switch S is open and no currents flow. Then the switch is closed.
7a) "hat is the current in the resistor R1 just after the switch is closed# 7b) $fter leaving the switch closed for a very long time, it is opened again. Kust after it is opened, what is the current in R1# $nswer 7a) 2.1 $ 7b) 2.: $ *ar 3D 21 &opyright - 21/ 0earson (ducation, nc.
