You hold a circular loop of wire at the equator. Consider

Problem 1CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Explain the difference between a magnetic field and a magnetic flux.

Problem 105IP Suppose the direction of the magnetic field is reversed. Everything else in the system remains the same, (a) Is the magnetic force exerted on the rod to the right, to the left, or zero? Explain, (b) Is the direction of the induced current clockwise, counterclockwise, or zero? Explain. (c) Suppose we now adjust the strength of the magnetic field until the speed of the rod is 2.49 m/s, keeping the force equal to 1.60 N. What is the new magnitude of the magnetic field?

Problem 2CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) A metal ring with a break in its perimeter is dropped from a field-free region of space into a region with a magnetic field. What effect does the magnetic field have on the ring?

Problem 3CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) In a common classroom demonstration, a magnet is dropped down a long, vertical copper tube. The magnet moves very slowly as it moves through the tube, taking several seconds to reach the bottom. Explain this behavior.

Problem 1P A 0.055-T magnetic field passes through a circular ring of radius 3.1 cm at an angle of 16° with the normal. Find the magnitude of the magnetic flux through the ring.

Problem 3P A magnetic field is oriented at an angle of 47° to the normal of a rectangular area 5.1 cm by 6.8 cm. If the magnetic flux through this surface has a magnitude of 4.8 × 10?5 T· m2, what is the strength of the magnetic field?

A uniform magnetic field of 0.0250 T points vertically upward. Find the magnitude of the magnetic flux through each of the five sides of the open-topped rectangular box shown in Figure 23–25, given that the dimensions of the box are \(L=32.5 \mathrm{~cm}, W=12.0 \mathrm{~cm} \text {, and } H=10.0 \mathrm{~cm}\) Equation Transcription: Text Transcription: L=32.5 cm, W=12.0 cm, and H=10.0 cm

Problem 4CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Many equal-arm balances have a small metal plate attached to one of the two arms. The plate passes between the poles of a magnet mounted in the base of the balance. Explain the purpose of this arrangement.

Problem 4P Find the magnitude of the magnetic flux through the floor of a house that measures 22 m by 18 m. Assume that the Earth's magnetic field at the location of the house has a horizontal component of 2.6 × 10?5 T pointing north, and a downward vertical component of 4.2 × 10?5 T.

Problem 5P The magnetic field produced by an MRI solenoid 2.5 m long and 1.2 m in diameter is 1.7 T. Find the magnitude of the magnetic flux through the core of this solenoid.

Referring to Conceptual Question 5, suppose the metal ring has a break in its circumference. Describe what happens when the switch is closed in this case.

Problem 6P At a certain location, the Earth's magnetic field has a magnitude of 5.9 × 10?5 T and points in a direction that is 72° below the horizontal. Find the magnitude of the magnetic flux through the top of a desk at this location that measures 130 cm by 82 cm.

Figure 23–23 shows a vertical iron rod with a wire coil of many turns wrapped around its base. A metal ring slides over the rod and rests on the wire coil. Initially the switch connecting the coil to a battery is open, but when it is closed, the ring flies into the air. Explain why this happens.

A metal rod of resistance R can slide without friction on two zero-resistance rails, as shown in Figure 23–24. The rod and the rails are immersed in a region of constant magnetic field pointing out of the page. Describe the motion of the rod when the switch is closed. Your discussion should include the effects of motional emf. Equation Transcription: Text Transcription: \vec{B}

Problem 7P A solenoid with 385 turns per meter and a diameter of 17.0 cm has a magnetic flux through its core of magnitude 1.28 × 10?4 T · m2. (a) Find the current in this solenoid, (b) How would your answer to part (a) change if the diameter of the solenoid were doubled? Explain.

Problem 9CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Recently, NASA tested a power generation system that involves connecting a small satellite to the space shuttle with a conducting wire several miles long. Explain how such a system can generate electrical power.

Problem 9P A 0.45-T magnetic field is perpendicular to a circular loop of wire with 53 turns and a radius of 15 cm. If the magnetic field is reduced to zero in 0.12 s, what is the magnitude of the induced emf?

Problem 8CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) A penny is placed on edge in the powerful magnetic field of an MR1 solenoid. If the penny is tipped over, it takes several seconds for it to land on one of its faces. Explain.

Problem 8P A single-turn square loop of side L is centered on the axis of a long solenoid. In addition, the plane of the square loop is perpendicular to the axis of the solenoid. The solenoid has 1250 turns per meter and a diameter of 6.00 cm, and carries a current of 2.50 A. Find the magnetic flux through the loop when (a) L = 3.00 cm, (b) L = 6.00 cm, and (c) L = 12.0 cm.

Problem 10CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) Explain what happens when the angular speed of the coil in an electric generator is increased.

Figure 23–26 shows the magnetic flux through a coil as a function of time. At what times shown in this plot do (a) the magnetic flux and (b) the induced emf have the greatest magnitude? Equation Transcription: Text Transcription: \Phi(W b) ________________

Problem 11CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) The inductor in an RL circuit determines how long it takes for the current to reach a given value, but it has no effect on the final value of the current. Explain.

Figure 23–27 shows the magnetic flux through a single-loop coil as a function of time. What is the induced emf in the coil at (a) \(t=0.050 \mathrm{~s}\), (b) \(t=0.15 \mathrm{~s}\), and (c) \(t=0.50 \mathrm{~s}\)? Equation Transcription: Text Transcription: t=0.050 s t=0.15 s t=0.50 s \Phi (Wb)

Problem 12CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book.) When the switch in a circuit containing an inductor is opened, it is common for a spark to jump across the contacts of the switch. Why?

A wire loop is placed in a magnetic field that is perpendicular to its plane. The field varies with time as shown in Figure 23–28. Rank the six regions of time in order of increasing magnitude of the induced emf. Indicate ties where appropriate.

Figure 23–29 shows four different situations in which a metal ring moves to the right with constant speed through a region with a varying magnetic field. The intensity of the color indicates the intensity of the field, and in each case the field either increases or decreases at a uniform rate from the left edge of the colored region to the right edge. The direction of the field in each region is indicated. For each of the four cases, state whether the induced emf is clockwise, counterclockwise, or zero.

The magnetic flux through a single-loop coil is given by Figure 23–27. (a) Is the magnetic flux at \(t=0.25 \mathrm{~s}\) greater than, less than, or the same as the magnetic flux at \(t=0.55 \mathrm{~s}\)? Explain. (b) Is the induced emf at \(t=0.25 \mathrm{~s}\) greater than, less than, or the same as the induced emf at \(t=0.55 \mathrm{~s}\)? Explain. (c) Calculate the induced emf at the times \(t=0.25 \mathrm{~s} \text { and } t=0.55 \mathrm{~s}\) Equation Transcription: Text Transcription: t=0.25 s t=0.55 s t=0.25 s t=0.55 s t=0.25 s and t=0.55 s \Phi (Wb)

Problem 16P A single conducting loop of wire has an area of 7.2 × 10?2 m2 and a resistance of 110 ?. Perpendicular to the plane of the loop is a magnetic field of strength 0.48 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.32 A?

Problem 17P The area of a 120-turn coil oriented with its plane perpendicular to a 0.20-T magnetic field is 0.050 m2. Find the average induced emf in this coil if the magnetic field reverses its direction in 0.34 s.

Consider a single-loop coil whose magnetic flux is given by Figure 23–26. (a) Is the magnitude of the induced emf in this coil greater near \(t=0.4 \mathrm{~s}\) or near \(t=0.5 \mathrm{~s}\)? Explain. (b) At what times in this plot do you expect the induced emf in the coil to have a maximum magnitude? Explain. (c) Estimate the induced emf in the coil at times near \(t=0.3 \mathrm{~s}, t=0.4 \mathrm{~s}, \text { and } t=0.5 \mathrm{~s}\). Equation Transcription: Text Transcription: t=0.4 s t=0.5 s t=0.3 s, t=0.4 s, and t=0.5 s \Phi (Wb)

Problem 18P An emf is induced in a conducting loop of wire 1.22 m long as its shape is changed from square to circular. Find the average magnitude of the induced emf if the change in shape occurs in 4.25 s and the local 0.125-T magnetic field is perpendicular to the plane of the loop.

Problem 19P A magnetic field increases from 0 to 0.25 T in 1.8 s. How many turns of wire are needed in a circular coil 12 cm in diameter to produce an induced emf of 6.0 V?

A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure 23–30. The magnetic field is zero above and below the region where it is finite. (a) For each of the three indicated locations (1, 2, and 3), is the induced current clockwise, counterclockwise, or zero? (b) Choose the best explanation from among the following: I. Clockwise at 1 to oppose the field; zero at 2 because the field is uniform; counterclockwise at 3 to try to maintain the field. II. Counterclockwise at 1 to oppose the field; zero at 2 because the field is uniform; clockwise at 3 to try to maintain the field. III. Clockwise at 1 to oppose the field; clockwise at 2 to maintain the field; clockwise at 3 to oppose the field.

A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure 23–30. The magnetic field is zero above and below the region where it is finite. (a) For each of the three indicated locations (1, 2, and 3), is the magnetic force exerted on the ring upward, downward, or zero? (b) Choose the best explanation from among the following: I. Upward at 1 to oppose entering the field; zero at 2 because the field is uniform; downward at 3 to help leaving the field. II. Upward at 1 to oppose entering the field; upward at 2 where the field is strongest; upward at 3 to oppose leaving the field. III. Upward at 1 to oppose entering the field; zero at 2 because the field is uniform; upward at 3 to oppose leaving the field.

Figure 23–31 shows two metal disks of the same size and material oscillating in and out of a region with a magnetic field. One disk is solid; the other has a series of slots. (a) Is the retarding effect of eddy currents on the solid disk greater than, less than, or equal to the retarding effect on the slotted disk? (b) Choose the best explanation from among the following: I. The solid disk experiences a greater retarding force because eddy currents in it flow freely and are not interrupted by the slots. II. The slotted disk experiences the greater retarding force because the slots allow more magnetic field to penetrate the disk. III. The disks are the same size and made of the same material; therefore, they experience the same retarding force. Equation Transcription: Text Transcription: \vec B

Consider the solid disk in Figure 23–31. When this disk has swung to the right as far as it can go, is the induced current in it a maximum or a minimum? Explain. Equation Transcription: Text Transcription: \vec B

(a) As the solid metal disk in Figure 23–31 swings to the right, from the region with no field into the region with a finite magnetic field, is the induced current in the disk clockwise, counterclockwise, or zero? (b) Choose the best explanation from among the following: I. The induced current is clockwise, since this produces a field within the disk in the same direction as the magnetic field that produced the current. II. The induced current is counterclockwise to generate a field within the disk that points out of the page. III. The induced current is zero because the disk enters a region where the magnetic field is uniform. Equation Transcription: Text Transcription: \vec B

Problem 25P A bar magnet with its north pole pointing downward is falling toward the center of a horizontal conducting ring. As viewed from above, is the direction of the induced current in the ring clockwise or counterclockwise? Explain.

A loop of wire is dropped and allowed to fall between the poles of a horseshoe magnet, as shown in Figure 23–32. State whether the induced current in the loop is clockwise or counterclockwise when (a) the loop is above the magnet and (b) the loop is below the magnet.

Suppose we change the situation shown in Figure 23–32 as follows: Instead of allowing the loop to fall on its own, we attach a string to it and lower it with constant speed along the path indicated by the dashed line. Is the tension in the string greater than, less than, or equal to the weight of the loop? Give specific answers for times when (a) the loop is above the magnet and (b) the loop is below the magnet. Explain in each case.

Rather than letting the loop fall downward in Figure 23–32, suppose we attach a string to it and raise it upward with constant speed along the path indicated by the dashed line. Is the tension in the string greater than, less than, or equal to the weight of the loop? Give specific answers for times when (a) the loop is below the magnet and (b) the loop is above the magnet. Explain in each case.

Figure 23–33 shows a current-carrying wire and a circuit containing a resistor R. (a) If the current in the wire is constant, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain. (b) If the current in the wire increases, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain.

Problem 31P A long, straight, current-carrying wire passes through the center of a circular coil. The wire is perpendicular to the plane of the coil, (a) If the current in the wire is constant, is the induced emf in the coil zero or nonzero? Explain, (b) If the current in the wire increases, is the induced emf in the coil zero or nonzero? Explain, (c) Does your answer to part (b) change if the wire no longer passes through the center of the coil but is still perpendicular to its plane? Explain.

Consider the physical system shown in Figure 23–33. If the current in the wire changes direction, is the induced current in the circuit clockwise, counterclockwise, or zero? Explain.

Figure 23–34 shows a circuit containing a resistor and an uncharged capacitor. Pointing into the plane of the circuit is a uniform magnetic field \(\vec{B}\). If the magnetic field reverses direction in a short period of time, which plate of the capacitor (top or bottom) becomes positively charged? Explain. Equation Transcription: Text Transcription: \vec B

Referring to Problem 32, which plate of the capacitor (top or bottom) becomes positively charged if the magnetic field increases in magnitude with time? Explain. Equation Transcription: Text Transcription: \vec{B} \vec{B}

A long, straight wire carries a current I, as indicated in Figure 23–35. Three small metal rings are placed near the current-carrying wire (A and C) or directly on top of it (B). If the current in the wire is increasing with time, indicate whether the induced emf in each of the rings is clockwise, counterclockwise, or zero. Explain your answer for each ring.

Problem 35P A conducting rod slides on two wires in a region with a magnetic field. The two wires arc not connected. Is a force required to keep the rod moving with constant speed? Explain.

Problem 36P A metal rod 0.76 m long moves with a speed Of 2.0 m/s perpendicular to a magnetic field. If the induced emf between the ends of the rod is 0.45 V, what is the strength of the magnetic field?

Problem 37P A Boeing KC-135A airplane has a wingspan of 39.9 m and flies at constant altitude in a northerly direction with a speed of 850 km/h. If the vertical component of the Earth's magnetic field is 5.0 × 10?6 T, and its horizontal component is 1.4 × 10?6 T, what is the induced emf between the wing tips?

Figure 23–36 shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance \(L=0.450 \mathrm{~m}\). The rails are connected by a \(12.5-\Omega\) resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T. (a) Find the speed at which the bar must be moved to produce a current of 0.155 Ain the resistor. (b) Would your answer to part (a) change if the bar was moving to the left instead of to the right? Explain. Equation Transcription: Text Transcription: L=0.450 m 12.5- \Omega \vec A

Referring to part (a) of Problem 38, (a) find the force that must be exerted on the rod to maintain a constant current of 0.155 A in the resistor. (b) What is the rate of energy dissipation in the resistor? (c) What is the mechanical power delivered to the rod? Figure 23–36 shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance \(L=0.450 m\). The rails are connected by a \(12.5-\Omega\) resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T. (a) Find the speed at which the bar must be moved to produce a current of 0.155 Ain the resistor. (b) Would your answer to part (a) change if the bar was moving to the left instead of to the right? Explain. Equation Transcription: Text Transcription: \vec{B} \vec{v} L=0.450 m 12.5-\Omega

(a) Find the current that flows in the circuit shown in Example 23–3. (b) What speed must the rod have if the current in the circuit is to be 1.0 A?

Problem 41P Suppose the mechanical power delivered to the rod in Example is 8.9 W. Find (a) the current in the circuit and (b) the speed of the rod.

Problem 42P The maximum induced em f in a generator rotating at 210 rpm is 45 V. Flow fast must the rotor of the generator rotate if it is to generate a maximum induced emf of 55 V?

Problem 44P A 1.6-m wire is wound into a coil with a radius of 3.2 cm. If this coil is rotated at 85 rpm in a 0.075-T magnetic field, what is its maximum emf?

Problem 45P A circular coil with a diameter of 22.0 cm and 155 turns rotates about a vertical axis with an angular speed of 1250 rpm. The only magnetic field in this system is that of the Earth. At the location of the coil, the horizontal component of the magnetic field is 3.80 × 10-5 T, and the vertical component is 2.85 × 10?5 T. (a) Which component of the magnetic field is important when calculating the induced emf in this coil? Explain, (b) Find the maximum emf induced in the coil.

Problem 43P A rectangular coil 25 cm by 35 cm has 120 turns. This coil produces a maximum emf of 65 V when it rotates with an angular speed of 190 rad/s in a magnetic field of strength B. Find the value of B.

Problem 46P A generator is designed to produce a maximum emf of 170 V while rotating with an angular speed of 3600 rpm. Each coil of the generator has an area of 0.016 m2. If the magnetic field used in the generator has a magnitude of 0.050 T, how many turns of wire are needed?

Problem 47P Find the induced em f when the current ill a 45.0-mH inductor increases from 0 to 515 mA in 16.5 ms.

Problem 48P How many turns should a solenoid of cross-sectional area 0.035 m2 and length 0.22 m have if its inductance is to be 45 mH?

Problem 49P The inductance of a solenoid with 450 turns and a length of 24 cm is 7.3 mH. (a) What is the cross-sectional area of the solenoid? (b) What is the induced emf in the solenoid if its current drops from 3.2 A to 0 in 55 ms?

Problem 50P Determine the inductance of a solenoid with 640 turns in a length of 25 cm. The circular cross section of the solenoid has a radius of 4.3 cm.

Problem 51P A solenoid with a cross-sectional area of 1.81 × 10?3 m2 is 0.750 m long and has 455 turns per meter. Find the induced emf in this solenoid if the current in it is increased from 0 to 2.00 A in 45.5 ms.

Problem 52P A solenoid has N turns of area A distributed uniformly along its length, ?. When the current in this solenoid increases at the rate of 2.0 A/s, an induced emf of 75 mV is observed, (a) What is the inductance of this solenoid? (b) Suppose the spacing between coils is doubled. The result is a solenoid that is twice as long but with the same area and number of turns. Will the induced emf in this new solenoid be greater than, less than, or equal to 75 mV when the current changes at the rate of 2.0 A/s? Explain, (c) Calculate the induced emf for part (b).

Problem 53P How long does it take for the current in an RL circuit with R = 130 ? and L = 68 mH to reach half its final value?

The four electric circuits shown in Figure 23–37 have identical batteries, resistors, and inductors. Rank the circuits in order of increasing current supplied by the battery long after the switch is closed. Indicate ties where appropriate.

The circuit shown in Figure 23–38 consists of a \(6.0-V\) battery, a \(37-m H\) inductor, and four \(55-\Omega\) resistors. (a) Find the characteristic time for this circuit. What is the current supplied by this battery (b) two characteristic time intervals after closing the switch and (c) a long time after the switch is closed? Equation Transcription: Text Transcription: 6.0-V 37-m H 55-\Omega

Problem 56P The current in an RL circuit increases to 95% of its filial value 2.24 s after the switch is closed, (a) What is the time constant for this circuit? (b) If the inductance in the circuit is 0.275 H, what is the resistance?

Consider the RL circuit shown in Figure 23–39. When the switch is closed, the current in the circuit is observed to increase from 0 to 0.32 A in \(0.15 s\). (a) What is the inductance L? (b) How long after the switch is closed does the current have the value \(0.50 A\)? (c) What is the maximum current that flows in this circuit? Equation Transcription: Text Transcription: 0.15 s 0.50 A 9.0 V 5.5 \Omega

Problem 58P The number of turns per meter in a solenoid of fixed length is doubled. At the same time, the current in the solenoid is halved. Does the energy stored in the inductor increase, decrease, or stay the same? Explain.

Problem 60P A solenoid is 1.5 m long and has 470 turns per meter. What is the cross-sectional area of this solenoid if it stores 0.31 J of energy when it carries a current of 12 A?

Consider the circuit shown in Figure 23–39. Assuming the inductor in this circuit has the value \(L=6.1 \mathrm{mH}\) , how much energy is stored in the inductor after the switch has been closed a long time? Equation Transcription: Text Transcription: L=6.1 mH

Problem 61P In the Alcator fusion experiment at MIT, a magnetic field of 50.0 T is produced, (a) What is the magnetic energy density in this field? (b) Find the magnitude of the electric field that would have the same energy density found in part (a).

Suppose the resistor in Figure 23–40 has the value \(R=14 \Omega\) and that the switch is closed at time \(t=0\) much energy is stored in the inductor at the time \(t=\tau\) much energy is stored in the inductor at the time . (a) How ? (b) How \(t=2 \tau\) ? (c) If the value of R is increased, does the characteristic time, \(\tau\) , increase or decrease? Explain. Equation Transcription: Text Transcription: R=14 \Omega t=0 t=\tau t=2 \tau \tau

After the switch in Figure 23–40 has been closed for a long time, the energy stored in the inductor is \(0.110 \mathrm{~J}\). (a) What is the value of the resistance R? (b) If it is desired that more energy be stored in the inductor, should the resistance R be greater than or less than the value found in part (a)? Explain. Equation Transcription: Text Transcription: 0.110 J 62.0 mH 12 V 7.50 \Omega

Consider the circuit shown in Figure 23–38, which contains a \(6.0-V\) battery, a \(37-m H\) inductor, and four \(55-\Omega\) resistors. (a) Is more energy stored in the inductor just after the switch is closed or long after the switch is closed? Explain. (b) Calculate the energy stored in the inductor one characteristic time interval after the switch is closed. (c) Calculate the energy stored in the inductor long after the switch is closed. Equation Transcription: Text Transcription: 6.0-V 37-mH 55-\Omega

Problem 66P Transformer 1 has a primary voltage Vp, and a secondary voltage Vs. Transformer 2 has twice the number of turns on both its primary and secondary coils compared with transformer 1. If the primary voltage on transformer 2 is 2Vp, what is its secondary voltage? Explain.

Problem 65P You would like to store 9.9 J of energy in the magnetic field of a solenoid. The solenoid has 580 circular turns of diameter 7.2 cm distributed uniformly along its 28-cm length, (a) How much current is needed? (b) What is the magnitude of the magnetic field inside the solenoid? (c) What is the energy density (energy/volume) inside the solenoid?

Problem 67P Transformer 1 has a primary current Ip and a secondary current Is. Transformer 2 has twice as many turns on its primary coil as transformer 1, and both transformers have the same number of turns on the secondary coil. If the primary current on transformer 2 is 3Ip, what is its secondary current? Explain.

Problem 69P A disk drive plugged into a 120-V outlet operates on a voltage of 9.0 V. The transformer that powers the disk drive has 125 turns on its primary coil, (a) Should the number of turns on the secondary coil be greater than or less than 125? Explain, (b) Find the number of turns on the secondary coil.

Problem 68P The electric motor in a toy train requires a voltage of 3.0 V. Find the ratio of turns on the primary coil to turns on the secondary coil in a transformer that will step the 110-V household voltage down to 3.0 V.

Problem 70P A transformer with a turns ratio (secondary/primary) of 1:18 is used to step down the voltage from a 120-V wall socket to be used in a battery recharging unit. What is the voltage supplied to the recharger?

Problem 72P A step-down transformer produces a voltage of 6.0 V across the secondary coil when the voltage across the primary coil is 120 V. What voltage appears across the primary coil of this transformer if 120 V is applied to the secondary coil?

Problem 71P A neon sign that requires a voltage of 11,000 V is plugged into a 120-V wall outlet. What turns ratio (secondary/primary) must a transformer have to power the sign?

Problem 73P A step-up transformer has 25 turns on the primary coil and 750 turns on the secondary coil. If this transformer is to produce an output of 4800 V with a 12-mA current, what input current and voltage are needed?

Problem 74GP An airplane flies level to the ground toward the north pole, (a) Is the induced emf from wing tip to wing tip when the plane is a t the equator greater them, less than, or equal to the wing-tip-to-wing-tip emf when it is at the latitude of New York? (b) Choose the best explanation from among the following: I. The induced emf is the same because the strength of the Earth's magnetic field is the same at the equator and at New York. II. The induced emf is greater at New York because the vertical component of the Earth's magnetic field is greater there than at the equator. III. The induced emf is less at New York because at the equator the plane is flying parallel to the magnetic field lines.

Problem 75GP You hold a circular loop of wire at the north magnetic pole of the Earth. Consider the magnetic flux through this loop due to the Earth's magnetic field. Is the flux when the normal to the loop points horizontally greater than, less than, or equal to the flux when the normal points vertically downward? Explain.

Problem 76GP You hold a circular loop of wire at the equator. Consider the magnetic flux through this loop due to the Earth's magnetic field. Is the flux when the normal to the loop points north greater than, less than, or equal to the flux when the normal points vertically upward? Explain.

The inductor shown in Figure 23–41 is connected to an electric circuit with a changing current. At the moment in question, the inductor has an induced emf with the indicated direction. Is the current in the circuit at this time increasing and to the right, increasing and to the left, decreasing and to the right, or decreasing and to the left?

Problem 78GP The Voyager I spacecraft moves through interstellar space with a speed of 8.0 × 103 m/s. The magnetic field in this region of space has a magnitude of 2.0 × 10-10 T. Assuming that the 5.0-m-long antenna on the spacecraft is at right angles to the magnetic field, find the induced emf between its ends.

Problem 79GP The coils used to measure the movements of a blowfly, as described in Section 23-5, have a diameter of 2.0 mm. In addition, the fly is immersed in a magnetic field of magnitude 0.15 mT. Find the maximum magnetic flux experienced by one of these coils.

Computerized jaw tracking, or electrognathography (EGN), is an important tool for diagnosing and treating temporomandibular disorders (TMDs) that affect a person’s ability to bite effectively. The first step in applying EGN is to attach a small permanent magnet to the patient’s gum below the lower incisors. Then, as the jaw undergoes a biting motion, the resulting change in magnetic flux is picked up by wire coils placed on either side of the mouth, as shown in Figure 23–42. Suppose this person’s jaw moves to her right and that the north pole of the permanent magnet also points to her right. From her point of view, is the induced current in the coil to (a) her right and (b) her left clockwise or counterclockwise? Explain.

A rectangular loop of wire \(24 \mathrm{~cm} \text { by } 72 \mathrm{~cm}\) is bent into an L shape, as shown in Figure 23–43. The magnetic field in the vicinity of the loop has a magnitude of 0.035 T and points in a direction \(25^{\circ}\) below the y axis. The magnetic field has no x component. Find the magnitude of the magnetic flux through the loop. Equation Transcription: Text Transcription: 24 cm by 72 cm 25°

Problem 84GP A car with a vertical radio antenna 85 cm long drives due east at 25 m/s. The Earth's magnetic field at this location has a magnitude of 5.9 × 10?5 T and points northward, 72° below the horizontal, (a) Ts the top or the bottom of the antenna at the higher potential? Explain, (b) Find the induced emf between the ends of the antenna.

A circular loop with a radius of \(3.7 \mathrm{~cm}\) lies in the x-y plane. The magnetic field in this region of space is uniform and given by \(\bar{B}=(0.43 T) \hat{x}+(-0.11 T) \hat{y}+(0.52 T) \hat{z}\). (a) What is the magnitude of the magnetic flux through this loop? (b) Suppose we now increase the x component of \(\bar{B}\), leaving the other components unchanged. Does the magnitude of the magnetic flux increase, decrease, or stay the same? Explain. (c) Suppose, instead, that we increase the z component of \(\bar{B}\) , leaving the other components unchanged. Does the magnitude of the magnetic flux increase, decrease, or stay the same? Explain. Equation Transcription: Text Transcription: 3.7 cm \bar B=(0.43 T) \hat x+(-0.11 T) \hat y+(0.52 T) \hat z \bar B \bar B

Problem 83GP Consider a rectangular loop of wire 5.8 cm by 8.2 cm in a uniform magnetic field of magnitude 1.3 T. The loop is rotated from a position of zero magnetic flux to a position of maximum flux in 21 ms. What is the average induced emf in the loop?

Problem 85GP The rectangular coils in a 325-turn generator are 11 cm by 17 cm. What is the maximum emf produced by this generator when it rotates with an angular speed of 525 rpm in a magnetic field of 0.45 T?

Problem 86GP A cubical box 22 cm 011 a side is placed in a uniform 0.35-T magnetic field. Find the net magnetic flux through the box.

Transcranial Magnetic Stimulation Transcranial magnetic stimulation (TMS) is a noninvasive method for studying brain function, and possibly for treatment as well. In this technique, a conducting loop is held near a person’s head, as shown in Figure 23–44. When the current in the loop is changed rapidly, the magnetic field it creates can change at the rate of \(3.00 \times 10^{4} \mathrm{~T} / \mathrm{s}\). This rapidly changing magnetic field induces an electric current in a restricted region of the brain that can cause a finger to twitch, bright spots to appear in the visual field (magnetophosphenes), or a feeling of complete happiness to overwhelm a person. If the magnetic field changes at the previously mentioned rate over an area of \(1.13 \times 10^{-2} \mathrm{~m}^{2}\) , what is the induced emf? Equation Transcription: Text Transcription: 3.00 x 104 T/s 1.13 x 10-2 m2

Amagnetic field with the time dependence shown in Figure 23–45 is at right angles to a 155-turn circular coil with a diameter of \(3.75 \mathrm{~cm}\). What is the induced emf in the coil at (a) \(t=2.50 \mathrm{~ms}\) (b) \(t=7.50 \mathrm{~ms}\), (c) \(t=15.0 \mathrm{~ms}\) , and (d) \(t=25.0 \mathrm{~ms}\)? Equation Transcription: Text Transcription: 3.75 cm t=2.50 ms t=7.50 ms t=15.0 ms t=25.0 ms

Problem 89GP You would like to construct a 50.0-mH inductor by wrapping insulated copper wire (diameter = 0.0332 cm) onto a tube with a circular cross section of radius 2.67 cm. What length of wire is required if it is wrapped onto the tube in a single, close- packed layer?

Problem 90GP The time constant of an RL circuit with L = 25 mH is twice the time constant of an RC circuit with C = 45 ? F. Both circuits have the same resistance R. Find (a) the value of R and (b) the time constant of the RL circuit.

Problem 91GP A 6.0-V battery is connected in series with a 29-mH inductor a 110-? resistor, and an open switch, (a) How long after the switch is closed will the current in the circuit be equal to 12 mA? (b) How much energy is stored in the inductor when the current reaches its maximum value?

Problem 93GP Suppose the fly described in Problem 79 turns through an angle of 90° in 37 ms. If the magnetic flux through one of the coils on the insect goes from a maximum to zero during this maneuver, and the coil has 85 turns of wire, find the magnitude of the induced emf.

Problem 92GP A 9.0-V battery is connected in series with a 31-mH inductor, a 180-?. resistor, and an open switch, (a) What is the current in the circuit 0.120 ms after the switch is closed? (b) How much energy is stored in the inductor at this time?

A conducting rod of mass m is in contact with two vertical conducting rails separated by a distance L, as shown in Figure 23–46. The entire system is immersed in a magnetic field of magnitude B pointing out of the page. Assuming the rod slides without friction, (a) describe the motion of the rod after it is released from rest. (b) What is the direction of the induced current (clockwise or counterclockwise) in the circuit? (c) Find the speed of the rod after it has fallen for a long time. Equation Transcription: Text Transcription: \vec B \vec v

A single-turn rectangular loop of width W and length L moves parallel to its length with a speed \(\sigma\). The loop moves from a region with a magnetic field \(\bar{B}\) perpendicular to the plane of the loop to a region where the magnetic field is zero, as shown in Figure 23–47. Find the rate of change in the magnetic flux through the loop (a) before it enters the region of zero field, (b) just after it enters the region of zero field, and (c) once it is fully within the region of zero field. (d) For each of the cases considered in parts (a), (b), and (c), state whether the induced current in the loop is clockwise, counterclockwise, or zero. Explain in each case. Equation Transcription: Text Transcription: \sigma \bar{B} \vec{B}

The switch in the circuit shown in Figure 23–48 is open initially. (a) Find the current in the circuit a long time after the switch is closed. (b) Describe the behavior of the lightbulb from the time the switch is closed until the current reaches the value found in part (a). (c) Now, suppose the switch is opened after having been closed for a long time. If the inductor is large, it is observed that the light flashes brightly and then burns out. Explain this behavior. (d) Find the voltage across the lightbulb just before and just after the switch is opened. Equation Transcription: Text Transcription: \varepsilon R_{1} R_{2}

Problem 97GP An electric field E and a magnetic field B have the same energy density, (a) Express the ratio E/B in terms of the fundamental constants ?0 and ?0. (b) Evaluate E/B numerically, and compare your result with the speed of light.

Suppose the downward vertical component of the magnetic field increases as a car drives over a loop detector. As viewed from above, is the induced current in the loop clockwise, counterclockwise, or zero?

A car drives onto a loop detector and increases the downward component of the magnetic field within the loop from \(1.2 \times 10^{-5} T \text { to } 2.6 \times 10^{-5} T \text { in } 0.38 \mathrm{~s}\). What is the induced emf in the detector if it is circular, has a radius of 0.67 m, and consists of four loops of wire? 1. \(0.66 \times 10^{-4} \mathrm{~V}\) B. \(0.66 \times 10^{-4} \mathrm{~V}\) C. \(2.1 \times 10^{-4} \mathrm{~V}\) D. \(6.2 \times 10^{-4} \mathrm{~V}\) Equation Transcription: Text Transcription: 1.2 x 10^-5 T to 2.6 x 10^-5 T in 0.38 s 0.66 x 10^-4 V 0.66 x 10^-4 V 2.1 x 10^-4 V 6.2 x 10^-4 V

A truck drives onto a loop detector and increases the downward component of the magnetic field within the loop from T to the larger value B in 0.38 s. The detector is circular, has a radius of 0.67 m, and consists of three loops of wire. What is B, given that the induced emf is \(8.1 \times 10^{-4} \mathrm{~V}\) A. \(3.6 \times 10^{-5} \mathrm{~T}\) B. \(7.3 \times 10^{-5} \mathrm{~T}\) C. \(8.5 \times 10^{-5} \mathrm{~T}\) D. \(24 \times 10^{-5} \mathrm{~T}\) Equation Transcription: Text Transcription: 8.1 x 10^-4 V 3.6 x 10^-5 T 7.3 x 10^-5 T 8.5 x 10^-5 T 24 x 10^-5 T

Suppose a motorcycle increases the downward component of the magnetic field within a loop only from \(1.2 \times 10^{-5} \mathrm{~T} \text { to } 1.9 \times 10^{-5} \mathrm{~T}\). The detector is square, is 0.75 m on a side, and has four loops of wire. Over what period of time must the magnetic field increase if it is to induce an emf of \(1.4 \times 10^{-4} \mathrm{~V}\)? A. 0.028 s B. 0.028 s C. 0.028 s D. 0.028 s Equation Transcription: Text Transcription: 1.2 x 10^-5T to 1.9 x 10^-5 T 1.4 x 10^-4V

Problem 102IP Suppose the ring is initially to the left of the field region, where there is no field, and is moving to the right. When the ring is partway into the field region, (a) is the induced current in the ring clockwise, counterclockwise, or zero, and (b) is the magnetic force exerted on the ring to the right, to the left, or zero? Explain.

Problem 103IP Suppose the ring is completely inside the field region initially and is moving to the right, (a) Is the induced current in the ring clockwise, counterclockwise, or zero, and (b) is the magnetic force on the ring to the right, to the left, or zero? Explain. The ring now begins to emerge from the field region, still moving to the right, (c) Is the induced current in the ring clockwise, counterclockwise, or zero, and (d) is the magnetic force on the ring to the right, to the left, or zero? Explain.

Problem 104IP (a) What external force is required to give the rod a speed of 3.49 m/s, every tiling else remaining the same? (b) What is the current in the circuit in this case?