A 0.80-m aluminum bar is held with its length parallel to

A 0.80-m aluminum bar is held with its length parallel to the east west direction and dropped from a bridge. Just before the bar hits the river below, its speed is 22 m/s, and the emf induced across its length is 6.5 3 1024 V. Assuming the horizontal component of the earths magnetic fi eld at the location of the bar points directly north, (a) determine the magnitude of the horizontal component of the earths magnetic fi eld, and (b) state whether the east end or the west end of the bar is positive.

Near San Francisco, where the vertically downward component of the earths magnetic fi eld is 4.8 3 1025 T, a car is traveling forward at 25 m/s. The width of the car is 2.0 m. (a) Find the emf induced between the two sides of the car. (b) Which side of the car is positivethe drivers side or the passengers side?

In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a 2.0 3 104 -m length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of 7.6 3 103 m/s, and the magnitude of the earths magnetic fi eld at the location of the wire was 5.1 3 1025 T. If the wire had moved perpendicular to the earths magnetic fi eld, what would have been the motional emf generated between the ends of the wire?

The drawing shows a type of fl ow meter that can be used to measure the speed of blood in situations when a blood vessel is suffi ciently exposed (e.g., during surgery). Blood is conductive enough that it can be treated as a moving conductor. When it fl ows perpendicularly with respect to a magnetic fi eld, as in the drawing, electrodes can be used to measure the small voltage that develops across the vessel. Suppose that the speed of the blood is 0.30 m/s and the diameter of the vessel is 5.6 mm. In a 0.60-T magnetic fi eld what is the magnitude of the voltage that is measured with the electrodes in the drawing?

The drawing shows three identical rods (A, B, and C) moving in diff erent planes. A constant magnetic fi eld of magnitude 0.45 T is directed along the 1y axis. The length of each rod is L 5 1.3 m, and the rods each have the same speed, vA 5 vB 5 vC 5 2.7 m/s. For each rod, fi nd the magnitude of the motional emf, and indicate which end (1 or 2) of the rod is positive.

Two circuits contain an emf produced by a moving metal rod, like that shown in Figure 22.4b. The speed of the rod is the same in each circuit, but the bulb in circuit 1 has one-half the resistance of the bulb in circuit 2. The circuits are otherwise identical. The resistance of the light bulb in circuit 1 is 55 V, and that in circuit 2 is 110 V. Determine (a) the ratio %1/%2 of the emfs and (b) the ratio I1/I2 of the currents in the circuits. (c) If the speed of the rod in circuit 1 were twice that in circuit 2, what would be the ratio P1/P2 of the powers in the circuits?

Refer to the drawing that accompanies Check Your Understanding Question 14. Suppose that the voltage of the battery in the circuit is 3.0 V, the magnitude of the magnetic fi eld (directed perpendicularly into the plane of the paper) is 0.60 T, and the length of the rod between the rails is 0.20 m. Assuming that the rails are very long and have negligible resistance, fi nd the maximum speed attained by the rod after the switch is closed.

Multiple-Concept Example 2 discusses the concepts that are used in this problem. Suppose that the magnetic fi eld in Figure 22.5 has a magnitude of 1.2 T, the rod has a length of 0.90 m, and the hand keeps the rod moving to the right at a constant speed of 3.5 m/s. If the current in the circuit is 0.040 A, what is the average power being delivered to the circuit by the hand?

Suppose that the light bulb in Figure 22.4b is a 60.0-W bulb with a resistance of 240 V. The magnetic fi eld has a magnitude of 0.40 T, and the length of the rod is 0.60 m. The only resistance in the circuit is that due to the bulb. What is the shortest distance along the rails that the rod would have to slide for the bulb to remain lit for one-half second?

Review Conceptual Example 3 and Figure 22.7b. A conducting rod slides down between two frictionless vertical copper tracks at a constant speed of 4.0 m/s perpendicular to a 0.50-T magnetic fi eld. The resistance of the rod and tracks is negligible. The rod maintains electrical contact with the tracks at all times and has a length of 1.3 m. A 0.75-V resistor is attached between the tops of the tracks. (a) What is the mass of the rod? (b)Find the change in the gravitational potential energy that occurs in a time of 0.20 s (c)Find the electrical energy dissipated in the resistor in 0.20 s.

The drawing shows two surfaces that have the same area. A uniform magnetic fi eld B B fi lls the space occupied by these surfaces, and it is oriented parallel to the yz plane as shown. Find the ratio Fxz/Fxy of the magnetic fl uxes that pass through the surfaces.

Two fl at surfaces are exposed to a uniform, horizontal magnetic fi eld of magnitude 0.47 T. When viewed edge-on, the fi rst surface is tilted at an angle of 12 from the horizontal, and a net magnetic fl ux of 8.4 3 1023 Wb passes through it. The same net magnetic fl ux passes through the second surface. (a) Determine the area of the fi rst surface. (b) Find the smallest possible value for the area of the second surface.

A standard door into a house rotates about a vertical axis through one side, as defi ned by the doors hinges. A uniform magnetic fi eld is parallel to the ground and perpendicular to this axis. Through what angle must the door rotate so that the magnetic fl ux that passes through it decreases from its maximum value to one-third of its maximum value?

A loop of wire has the shape shown in the drawing. The top part of the wire is bent into a semicircle of radius r 5 0.20 m. The normal to the plane of the loop is parallel to a constant magnetic fi eld (f 5 08) of magnitude 0.75 T. What is the change DF in the magnetic fl ux that passes through the loop when, starting with the position shown in the drawing, the semicircle is rotated through half a revolution?

A magnetic fi eld has a magnitude of 0.078 T and is uniform over a circular surface whose radius is 0.10 m. The fi eld is oriented at an angle of f 5 258 with respect to the normal to the surface. What is the magnetic fl ux through the surface?

A square loop of wire consisting of a single turn is perpendicular to a uniform magnetic fi eld. The square loop is then re-formed into a circular loop, which also consists of a single turn and is also perpendicular to the same magnetic fi eld. The magnetic fl ux that passes through the square loop is 7.0 3 1023 Wb. What is the fl ux that passes through the circular loop?

A fi ve-sided object, whose dimensions are shown in the drawing, is placed in a uniform magnetic fi eld. The magnetic fi eld has a magnitude of 0.25 T and points along the positive y direction. Determine the magnetic fl ux through each of the fi ve sides.

A magnetic fi eld passes through a stationary wire loop, and its magnitude changes in time according to the graph in the drawing. The direction of the fi eld remains constant, however. There are three equal time intervals indicated in the graph: 03.0 s, 3.06.0 s, and 6.09.0 s. The loop consists of 50 turns of wire and has an area of 0.15 m2 . The magnetic fi eld is oriented parallel to the normal to the loop. For purposes of this problem, this means that f 5 0 in Equation 22.2. (a) For each interval, determine the induced emf. (b) The wire has a resistance of 0.50 V. Determine the induced current for the fi rst and third intervals.

A rectangular loop of wire with sides 0.20 and 0.35 m lies in a plane perpendicular to a constant magnetic fi eld (see part a of the drawing). The magnetic fi eld has a magnitude of 0.65 T and is directed parallel to the normal of the loops surface. In a time of 0.18 s, one-half of the loop is then folded back onto the other half, as indicated in part b of the drawing. Determine the magnitude of the average emf induced in the loop.

Magnetic resonance imaging (MRI) is a medical technique for producing pictures of the interior of the body. The patient is placed within a strong magnetic fi eld. One safety concern is what would happen to the positively and negatively charged particles in the body fl uids if an equipment failure caused the magnetic fi eld to be shut off suddenly. An induced emf could cause these particles to fl ow, producing an electric current within the body. Suppose the largest surface of the body through which fl ux passes has an area of 0.032 m2 and a normal that is parallel to a magnetic fi eld of 1.5 T. Determine the smallest time period during which the fi eld can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V.

A circular coil (950 turns, radius 5 0.060 m) is rotating in a uniform magnetic fi eld. At t 5 0 s, the normal to the coil is perpendicular to the magnetic fi eld. At t 5 0.010 s, the normal makes an angle of f 5 45 with the fi eld because the coil has made one-eighth of a revolution. An average emf of magnitude 0.065 V is induced in the coil. Find the magnitude of the magnetic fi eld at the location of the coil.

The magnetic fl ux that passes through one turn of a 12-turn coil of wire changes to 4.0 from 9.0 Wb in a time of 0.050 s. The average induced current in the coil is 230 A. What is the resistance of the wire?

A constant magnetic fi eld passes through a single rectangular loop whose dimensions are 0.35 m 3 0.55 m. The magnetic fi eld has a magnitude of 2.1 T and is inclined at an angle of 658 with respect to the normal to the plane of the loop. (a) If the magnetic fi eld decreases to zero in a time of 0.45 s, what is the magnitude of the average emf induced in the loop? (b) If the magnetic fi eld remains constant at its initial value of 2.1 T, what is the magnitude of the rate DA/Dt at which the area should change so that the average emf has the same magnitude as in part (a)?

A uniform magnetic fi eld is perpendicular to the plane of a single-turn circular coil. The magnitude of the fi eld is changing, so that an emf of 0.80 V and a current of 3.2 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic fi eld (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What emf and current are induced in the square coil?

A copper rod is sliding on two conducting rails that make an angle of 198 with respect to each other, as in the drawing. The rod is moving to the right with a constant speed of 0.60 m/s. A 0.38-T uniform magnetic fi eld is perpendicular to the plane of the paper. Determine the magnitude of the average emf induced in the triangle ABC during the 6.0-s period after the rod has passed point A.

A fl at coil of wire has an area A, N turns, and a resistance R. It is situated in a magnetic fi eld, such that the normal to the coil is parallel to the magnetic fi eld. The coil is then rotated through an angle of 90, so that the normal becomes perpendicular to the magnetic fi eld. The coil has an area of 1.5 3 1023 m2 , 50 turns, and a resistance of 140 V. During the time while it is rotating, a charge of 8.5 3 1025 C fl ows in the coil. What is the magnitude of the magnetic fi eld?

A magnetic fi eld is passing through a loop of wire whose area is 0.018 m2 . The direction of the magnetic fi eld is parallel to the normal to the loop, and the magnitude of the fi eld is increasing at the rate of 0.20 T/s. (a) Determine the magnitude of the emf induced in the loop. (b) Suppose that the area of the loop can be enlarged or shrunk. If the magnetic fi eld is increasing as in part (a), at what rate (in m2 /s) should the area be changed at the instant when B 5 1.8 T if the induced emf is to be zero? Explain whether the area is to be enlarged or shrunk.

A fl at circular coil with 105 turns, a radius of 4.00 3 1022 m, and a resistance of 0.480 V is exposed to an external magnetic fi eld that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic fi eld is changing at a rate of DB/Dt 5 0.783 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic fi eld at the center of the coil that is produced by the induced current.

The drawing shows a coil of copper wire that consists of two semicircles joined by straight sections of wire. In part a the coil is lying fl at on a horizontal surface. The dashed line also lies in the plane of the horizontal surface. Starting from the orientation in part a, the smaller semicircle rotates at an angular frequency v about the dashed line, until its plane becomes perpendicular to the horizontal surface, as shown in part b. A uniform magnetic fi eld is constant in time and is directed upward, perpendicular to the horizontal surface. The fi eld completely fi lls the region occupied by the coil in either part of the drawing. The magnitude of the magnetic fi eld is 0.35 T. The resistance of the coil is 0.025 V, and the smaller semicircle has a radius of 0.20 m. The angular frequency at which the small semicircle rotates is 1.5 rad/s. Determine the average current I, if any, induced in the coil as the coil changes shape from that in part a of the drawing to that in part b. Be sure to include an explicit plus or minus sign along with your answer.

A conducting coil of 1850 turns is connected to a galvanometer, and the total resistance of the circuit is 45.0 V. The area of each turn is 4.70 3 1024 m2 . This coil is moved from a region where the magnetic fi eld is zero into a region where it is nonzero, the normal to the coil being kept parallel to the magnetic fi eld. The amount of charge that is induced to fl ow around the circuit is measured to be 8.87 3 1023 C. Find the magnitude of the magnetic fi eld.

Two 0.68-m-long conducting rods are rotating at the same speed in opposite directions, and both are perpendicular to a 4.7-T magnetic fi eld. As the drawing shows, the ends of these rods come to within 1.0 mm of each other as they rotate. Moreover, the fi xed ends about which the rods are rotating are connected by a wire, so these ends are at the same electric potential. If a potential diff erence of 4.5 3 103 V is required to cause a 1.0-mm spark in air, what is the angular speed (in rad/s) of the rods when a spark jumps across the gap?

Starting from the position indicated in the drawing, the semicircular piece of wire rotates through half a revolution in the direction shown. Which end of the resistor is positivethe left or the right end? Explain your reasoning.

The plane of a fl at, circular loop of wire is horizontal. An external magnetic fi eld is directed perpendicular to the plane of the loop. The magnitude of the external magnetic fi eld is increasing with time. Because of this increasing magnetic fi eld, an induced current is fl owing clockwise in the loop, as viewed from above. What is the direction of the external magnetic fi eld? Justify your conclusion

The drawing shows a straight wire carrying a current I. Above the wire is a rectangular loop that contains a resistor R. If the current I is decreasing in time, what is the direction of the induced current through the resistor Rleft-to-right or right-to-left?

The drawing depicts a copper loop lying fl at on a table (not shown) and connected to a battery via a closed switch. The current I in the loop generates the magnetic fi eld lines shown in the drawing. The switch is then opened and the current goes to zero. There are also two smaller conducting loops A and B lying fl at on the table, but not connected to batteries. Determine the direction of the induced current in (a) loop A and (b) loop B. Specify the direction of each induced current to be clockwise or counterclockwise when viewed from above the table. Provide a reason for each answer.

The drawing shows that a uniform magnetic fi eld is directed perpendicularly into the plane of the paper and fi lls the entire region to the left of the y axis. There is no magnetic fi eld to the right of the y axis. A rigid right triangle ABC is made of copper wire. The triangle rotates counterclockwise about the origin at point C. What is the direction (clockwise or counterclockwise) of the induced current when the triangle is crossing (a) the 1y axis, (b) the 2x axis, (c) the 2y axis, and (d) the 1x axis? For each case, justify your answer.

A circular loop of wire rests on a table. A long, straight wire lies on this loop, directly over its center, as the drawing illustrates. The current I in the straight wire is decreasing. In what direction is the induced current, if any, in the loop? Give your reasoning.

The drawing shows a bar magnet falling through a metal ring. In part a the ring is solid all the way around, but in part b it has been cut through. (a) Explain why the motion of the magnet in part a is retarded when the magnet is above the ring and below the ring as well. Draw any induced currents that appear in the ring. (b) Explain why the motion of the magnet is unaff ected by the ring in part b

A wire loop is suspended from a string that is attached to point P in the drawing. When released, the loop swings downward, from left to right, through a uniform magnetic fi eld, with the plane of the loop remaining perpendicular to the plane of the paper at all times. (a) Determine the direction of the current induced in the loop as it swings past the locations labeled I and II. Specify the direction of the current in terms of the points x, y, and z on the loop (e.g., x S y S z or z S y S x). The points x, y, and z lie behind the plane of the paper. (b) What is the direction of the induced current at the locations II and I when the loop swings back, from right to left? Provide reasons for your answers.

A 120.0-V motor draws a current of 7.00 A when running at normal speed. The resistance of the armature wire is 0.720 V. (a) Determine the back emf generated by the motor. (b) What is the current at the instant when the motor is just turned on and has not begun to rotate? (c) What series resistance must be added to limit the starting current to 15.0 A?

A generator has a square coil consisting of 248 turns. The coil rotates at 79.1 rad/s in a 0.170-T magnetic fi eld. The peak output of the generator is 75.0 V. What is the length of one side of the coil?

You need to design a 60.0-Hz ac generator that has a maximum emf of 5500 V. The generator is to contain a 150-turn coil that has an area per turn of 0.85 m2 . What should be the magnitude of the magnetic fi eld in which the coil rotates?

The maximum strength of the earths magnetic fi eld is about 6.9 3 1025 T near the south magnetic pole. In principle, this fi eld could be used with a rotating coil to generate 60.0-Hz ac electricity. What is the minimum number of turns (area per turn 5 0.022 m2 ) that the coil must have to produce an rms voltage of 120 V?

A vacuum cleaner is plugged into a 120.0-V socket and uses 3.0 A of current in normal operation when the back emf generated by the electric motor is 72.0 V. Find the coil resistance of the motor.

A generator uses a coil that has 100 turns and a 0.50-T magnetic fi eld. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. Assuming that each turn of the coil is a square (an approximation), determine the length of the wire from which the coil is made.

The coil of a generator has a radius of 0.14 m. When this coil is unwound, the wire from which it is made has a length of 5.7 m. The magnetic fi eld of the generator is 0.20 T, and the coil rotates at an angular speed of 25 rad/s. What is the peak emf of this generator?

Consult Multiple-Concept Example 11 for background material relating to this problem. A small rubber wheel on the shaft of a bicycle generator presses against the bike tire and turns the coil of the generator at an angular speed that is 38 times as great as the angular speed of the tire itself. Each tire has a radius of 0.300 m. The coil consists of 125 turns, has an area of 3.86 3 1023 m2 , and rotates in a 0.0900-T magnetic fi eld. The bicycle starts from rest and has an acceleration of 10.550 m/s2 . What is the peak emf produced by the generator at the end of 5.10 s?

A motor is designed to operate on 117 V and draws a current of 12.2 A when it fi rst starts up. At its normal operating speed, the motor draws a current of 2.30 A. Obtain (a) the resistance of the armature coil, (b) the back emf developed at normal speed, and (c) the current drawn by the motor at one-third of the normal speed.

The earths magnetic fi eld, like any magnetic fi eld, stores energy. The maximum strength of the earths fi eld is about 7.0 3 1025 T. Find the maximum magnetic energy stored in the space above a city if the space occupies an area of 5.0 3 108 m2 and has a height of 1500 m.

The current through a 3.2-mH inductor varies with time according to the graph shown in the drawing. What is the average induced emf during the time intervals (a) 02.0 ms, (b) 2.05.0 ms, and (c) 5.09.0 ms?

Two coils of wire are placed close together. Initially, a current of 2.5 A exists in one of the coils, but there is no current in the other. The current is then switched off in a time of 3.7 3 1022 s. During this time, the average emf induced in the other coil is 1.7 V. What is the mutual inductance of the two-coil system?

During a 72-ms interval, a change in the current in a primary coil occurs. This change leads to the appearance of a 6.0-mA current in a nearby secondary coil. The secondary coil is part of a circuit in which the resistance is 12 V. The mutual inductance between the two coils is 3.2 mH. What is the change in the primary current?

Mutual induction can be used as the basis for a metal detector. A typical setup uses two large coils that are parallel to each other and have a common axis. Because of mutual induction, the ac generator connected to the primary coil causes an emf of 0.46 V to be induced in the secondary coil. When someone without metal objects walks through the coils, the mutual inductance and, thus, the induced emf do not change much. But when a person carrying a handgun walks through, the mutual inductance increases. The change in emf can be used to trigger an alarm. If the mutual inductance increases by a factor of three, fi nd the new value of the induced emf

A constant current of I 5 15 A exists in a solenoid whose inductance is L 5 3.1 H. The current is then reduced to zero in a certain amount of time. (a) If the current goes from 15 to 0 A in a time of 75 ms, what is the emf induced in the solenoid? (b) How much electrical energy is stored in the solenoid? (c) At what rate must the electrical energy be removed from the solenoid when the current is reduced to 0 A in a time of 75 ms? Note that the rate at which energy is removed is the power

Suppose you wish to make a solenoid whose self-inductance is 1.4 mH. The inductor is to have a cross-sectional area of 1.2 3 1023 m2 and a length of 0.052 m. How many turns of wire are needed?

A long, current-carrying solenoid with an air core has 1750 turns per meter of length and a radius of 0.0180 m. A coil of 125 turns is wrapped tightly around the outside of the solenoid, so it has virtually the same radius as the solenoid. What is the mutual inductance of this system?

A 5.40 3 1025 H solenoid is constructed by wrapping 65 turns of wire around a cylinder with a cross-sectional area of 9.0 3 1024 m2 . When the solenoid is shortened by squeezing the turns closer together, the inductance increases to 8.60 3 1025 H. Determine the change in the length of the solenoid.

A long solenoid (cross-sectional area 5 1.0 3 1026 m2 , number of turns per unit length 5 2400 turns/m) is bent into a circular shape so it looks like a donut. This wire-wound donut is called a toroid. Assume that the diameter of the solenoid is small compared to the radius of the toroid, which is 0.050 m. Find the emf induced in the toroid when the current decreases to 1.1 A from 2.5 A in a time of 0.15 s.

Coil 1 is a fl at circular coil that has N1 turns and a radius R1. At its center is a much smaller fl at, circular coil that has N2 turns and radius R2. The planes of the coils are parallel. Assume that coil 2 is so small that the magnetic fi eld due to coil 1 has nearly the same value at all points covered by the area of coil 2. Determine an expression for the mutual inductance between these two coils in terms of m0, N1, R1, N2, and R2.

The battery charger for an MP3 player contains a step-down transformer with a turns ratio of 1:32, so that the voltage of 120 V available at a wall socket can be used to charge the battery pack or operate the player. What voltage does the secondary coil of the transformer provide?

The secondary coil of a step-up transformer provides the voltage that operates an electrostatic air fi lter. The turns ratio of the transformer is 50:1. The primary coil is plugged into a standard 120-V outlet. The current in the secondary coil is 1.7 3 1023 A. Find the power consumed by the air fi lter.

The rechargeable batteries for a laptop computer need a much smaller voltage than what a wall socket provides. Therefore, a transformer is plugged into the wall socket and produces the necessary voltage for charging the batteries. The batteries are rated at 9.0 V, and a current of 225 mA is used to charge them. The wall socket provides a voltage of 120 V. (a) Determine the turns ratio of the transformer. (b) What is the current coming from the wall socket? (c) Find the average power delivered by the wall socket and the average power sent to the batteries.

The resistances of the primary and secondary coils of a transformer are 56 and 14 V, respectively. Both coils are made from lengths of the same copper wire. The circular turns of each coil have the same diameter. Find the turns ratio Ns/Np.

A transformer consisting of two coils wrapped around an iron core is connected to a generator and a resistor, as shown in the drawing. There are 11 turns in the primary coil and 18 turns in the secondary coil. The peak voltage across the resistor is 67 V. What is the peak emf of the generator?

A step-down transformer (turns ratio 5 1:8) is used with an electric train to reduce the voltage from the wall receptacle to a value needed to operate the train. When the train is running, the current in the secondary coil is 1.6 A. What is the current in the primary coil?

In a television set the power needed to operate the picture tube comes from the secondary of a transformer. The primary of the transformer is connected to a 120-V receptacle on a wall. The picture tube of the television set uses 91 W, and there is 5.5 mA of current in the secondary coil of the transformer to which the tube is connected. Find the turns ratio Ns/Np of the transformer.

A generating station is producing 1.2 3 106 W of power that is to be sent to a small town located 7.0 km away. Each of the two wires that comprise the transmission line has a resistance per kilometer of 5.0 3 1022 V/km. (a) Find the power used to heat the wires if the power is transmitted at 1200 V. (b) A 100:1 step-up transformer is used to raise the voltage before the power is transmitted. How much power is now used to heat the wires?

Suppose there are two transformers between your house and the high-voltage transmission line that distributes the power. In addition, assume that your house is the only one using electric power. At a substation the primary coil of a step-down transformer (turns ratio 5 1:29) receives the voltage from the high-voltage transmission line. Because of your usage, a current of 48 mA exists in the primary coil of this transformer. The secondary coil is connected to the primary of another step-down transformer (turns ratio 5 1:32) somewhere near your house, perhaps up on a telephone pole. The secondary coil of this transformer delivers a 240-V emf to your house. How much power is your house using? Remember that the current and voltage given in this problem are rms values.

A generator is connected across the primary coil (Np turns) of a transformer, while a resistance R2 is connected across the secondary coil (Ns turns). This circuit is equivalent to a circuit in which a single resistance R1 is connected directly across the generator, without the transformer. Show that R1 5 (Np/Ns) 2 R2, by starting with Ohms law as applied to the secondary coil.

In each of two coils the rate of change of the magnetic fl ux in a single loop is the same. The emf induced in coil 1, which has 184 loops, is 2.82 V. The emf induced in coil 2 is 4.23 V. How many loops does coil 2 have?

When its coil rotates at a frequency of 280 Hz, a certain generator has a peak emf of 75 V. (a) What is the peak emf of the generator when its coil rotates at a frequency of 45 Hz? (b) Determine the frequency of the coils rotation when the peak emf of the generator is 180 V.

A planar coil of wire has a single turn. The normal to this coil is parallel to a uniform and constant (in time) magnetic fi eld of 1.7 T. An emf that has a magnitude of 2.6 V is induced in this coil because the coils area A is shrinking. What is the magnitude of DA/Dt, which is the rate (in m2 /s) at which the area changes?

Review Conceptual Example 9 as an aid in understanding this problem. A long, straight wire lies on a table and carries a current I. As the drawing shows, a small circular loop of wire is pushed across the top of the table from position 1 to position 2. Determine the direction of the induced current, clockwise or counterclockwise, as the loop moves past (a) position 1 and (b) position 2. Justify your answers.

In some places, insect zappers, with their blue lights, are a familiar sight on a summers night. These devices use a high voltage to electrocute insects. One such device uses an ac voltage of 4320 V, which is obtained from a standard 120.0-V outlet by means of a transformer. If the primary coil has 21 turns, how many turns are in the secondary coil?

A 3.0-mF capacitor has a voltage of 35 V between its plates. What must be the current in a 5.0-mH inductor so that the energy stored in the inductor equals the energy stored in the capacitor?

At its normal operating speed, an electric fan motor draws only 15.0% of the current it draws when it just begins to turn the fan blade. The fan is plugged into a 120.0-V socket. What back emf does the motor generate at its normal operating speed?

Parts a and b of the drawing show the same uniform and constant (in time) magnetic fi eld B B directed perpendicularly into the paper over a rectangular region. Outside this region, there is no fi eld. Also shown is a rectangular coil (one turn), which lies in the plane of the paper. In part a the long side of the coil (length 5 L) is just at the edge of the fi eld region, while in part b the short side (width 5 W) is just at the edge. It is known that L/W 5 3.0. In both parts of the drawing the coil is pushed into the fi eld with the same velocity v B until it is completely within the fi eld region. The magnitude of the average emf induced in the coil in part a is 0.15 V. What is its magnitude in part b?

Indicate the direction of the electric fi eld between the plates of the parallel plate capacitor shown in the drawing if the magnetic fi eld is decreasing in time. Give your reasoning.

A piece of copper wire is formed into a single circular loop of radius 12 cm. A magnetic fi eld is oriented parallel to the normal to the loop, and it increases from 0 to 0.60 T in a time of 0.45 s. The wire has a resistance per unit length of 3.3 3 1022 V/m. What is the average electrical energy dissipated in the resistance of the wire?

The purpose of this problem is to show that the work W needed to establish a fi nal current If in an inductor is W 5 1 2 LI 2 f (Equation 22.10). In Section 22.8 we saw that the amount of work DW needed to change the current through an inductor by an amount DI is DW 5 LI(DI), where L is the inductance. The drawing shows a graph of LI versus I. Notice that LI(DI) is the area of the shaded vertical rectangle whose height is LI and whose width is DI. Use this fact to show that the total work W needed to establish a current If is W 5 1 2 LI 2 f .

A solenoid has a cross-sectional area of 6.0 3 1024 m2 , consists of 400 turns per meter, and carries a current of 0.40 A. A 10-turn coil is wrapped tightly around the circumference of the solenoid. The ends of the coil are connected to a 1.5-V resistor. Suddenly, a switch is opened, and the current in the solenoid dies to zero in a time of 0.050 s. Find the average current induced in the coil.

A 60.0-Hz generator delivers an average power of 75 W to a single light bulb. When an induced current exists in the rotating coil of a generator, a torquecalled a countertorqueis exerted on the coil. Determine the maximum countertorque in the generator coil. (Hint: The peak current, peak emf, and maximum countertorque all occur at the same instant.)

A long solenoid of length 8.0 3 1022 m and cross-sectional area 5.0 3 1025 m2 contains 6500 turns per meter of length. Determine the emf induced in the solenoid when the current in the solenoid changes from 0 to 1.5 A during the time interval from 0 to 0.20 s.

A circular coil of radius 0.11 m contains a single turn and is located in a constant magnetic fi eld of magnitude 0.27 T. The magnetic fi eld has the same direction as the normal to the plane of the coil. The radius increases to 0.30 m in a time of 0.080 s. Concepts: (i) Why is there an emf induced in the coil? (ii) Does the magnitude of the induced emf depend on whether the area is increasing or decreasing? Explain. (iii) What determines the amount of current induced in the coil? (iv) If the coil is cut so it is no longer one continuous piece, are there an induced emf and an induced current? Explain. Calculations: (a) Determine the magnitude of the emf induced in the coil. (b) The coil has a resistance of 0.70 V. Find the magnitude of the induced current.

The graph in the fi gure shows the emf produced by a generator as a function of time t. The coil for the generator has an area of A 5 0.15 m2 and consists of N 5 10 turns. The coil rotates in a fi eld of magnitude 0.27 T. Concepts: (i) Can the period of the rotating coil be determined from the graph? (ii) The emf produced by a generator depends on its angular frequency. How is the angular frequency of the coil related to its period? (iii) Starting at t 5 0 s, how much time is required for the generator to produce its peak emf? Express the answer in terms of the period T of the motion (e.g., t 5 (0.1) T). (iv) How often does the polarity of the emf change in one cycle? Calculations: (a) Determine the period of the motion. (b) What is the angular frequency of the rotating coil? (c) Find the value of the emf when t 5 1 4 T, where T denotes the period of the coil motion. (d) What is the emf when t 5 0.025 s?