1cc. The four figures show a bar magnet and a low-voltage light bulb
connected to the ends of a conducting loop. The plane of the loop is
perpendicular to the dashed line. In case 1, the loop is stationary, and
the magnet is moving away from the loop. In case 2, the magnet is
stationary, and the loop is moving toward the magnet. In case 3, both
the magnet and the loop are stationary, but the area of the loop is
increasing. In case 4, the magnet is stationary, and the loop is
rotating about its center. In which of these situations will the bulb
light up?Case 1...Case 2...Case 3...Case 4...a) case 1b) cases 1 and 2c)
cases 1, 2, and 3d) cases 1, 2, and 4e) all four cases Get solution
1mcq. A solenoid with 200 turns and a cross-sectional area of 60 cm2 has a magnetic field of 0.60 T along its axis. If the field is confined within the solenoid and changes at a rate of 0.20 T/s, the magnitude of the induced potential difference in the solenoid will bea) 0.0020 V.b) 0.02 V.c) 0.001 V.d) 0.24 V. Get solution
2cc. A power supply is connected to loop 1 and an ammeter as shown in the figure. Loop 2 is close to loop 1 and is connected to a voltmeter. A graph of the current i through loop 1 as a function of time, t, is also shown in the figure. Which graph best describes the induced potential difference, ΔVind, in loop 2 as a function of time, t?...Graph 1...Graph 2...Graph 3...Graph 4...a) graph 1b) graph 2c) graph 3d) graph 4 Get solution
2mcq. The rectangular loop of wire in Figure 29.9 is pulled with a constant acceleration from a region of zero magnetic field into a region of a uniform magnetic field. During this process, the current induced in the loopa) will be zero.b) will be some constant value that is not zero.c) will increase linearly with time.d) will increase exponentially with time.e) will increase linearly with the square of the time.Figure 29.9 A wire loop (blue) is pulled out of a gap between two magnets... Get solution
3cc. A long wire carries a current, i, as shown in the figure. A square loop moves in the same plane as the wire, as indicated. In which cases will the loop have an induced current?Case 1...Case 2...Case 3...a) cases 1 and 2b) cases 1 and 3c) cases 2 and 3d) None of the loops will have an induced current.e) All of the loops will have an induced current. Get solution
3mcq. Which of the following will induce a current in a loop of wire in a uniform magnetic field?a) decreasing the strength of the fieldb) rotating the loop about an axis parallel to the fieldc) moving the loop within the fieldd) all of the abovee) none of the above Get solution
4cc. A metal bar is moving with constant velocity ... through a uniform magnetic field pointing into the page, as shown in the figure. Which of the following most accurately represents the charge distribution on the surface of the metal bar?...Distribution1...Distribution2...Distribution3...Distribution4...Distribution5...a) distribution 1b) distribution 2c) distribution 3d) distribution 4e) distribution 5 Get solution
4mcq. Faraday’s Law of Induction states thata) a potential difference is induced in a loop when there is a change in the magnetic flux through the loop.b) the current induced in a loop by a changing magnetic field produces a magnetic field that opposes this change in magnetic field.c) a changing magnetic field induces an electric field.d) the inductance of a device is a measure of its opposition to changes in current flowing through it.e) magnetic flux is the product of the average magnetic field and the area perpendicular to it that it penetrates. Get solution
5cc. A wire loop is placed in a uniform magnetic field. Over a period of 2 s, the loop is shrunk. Which statement about the induced potential difference is correct?...a) There will be some induced potential difference.b) There will be no induced potential difference because the loop changes size along one axis and not the other.c) There will be no induced potential difference because the loop is not closed.d) There will be no induced potential difference because the loop is shrinking. Get solution
5mcq. A conducting ring is moving from left to right through a uniform magnetic field, as shown in the figure. In which region(s) is there an induced current in the ring?...a) regions B and Db) regions B, C, and Dc) region Cd) regions A through E Get solution
6cc. Two identical coils are shown in the figure. Coil 1 has a current i flowing in the direction shown. When the switch in the circuit containing coil 1 is opened, what happens in coil 2?Coil 1...Coil 2...a) A current is induced in coil 2 that flows in direction 1.b) A current is induced in coil 2 that flows in direction 2.c) No current is induced in coil 2. Get solution
6mcq. A circular loop of wire moving in the xy-plane with a constant velocity in the negative x-direction enters a uniform magnetic field, which covers the region in which x ...a) The induced potential difference in the loop is at a maximum as the edge of the loop just enters the region with the magnetic field.b) The induced potential difference in the loop is at a maximum when one fourth of the loop is in the region with the magnetic field.c) The induced potential difference in the loop is at a maximum when the loop is halfway into the region with the magnetic field.d) The induced potential difference in the loop is constant from the instant the loop starts to enter the region with the magnetic field. Get solution
7cc. Consider the RL circuit shown in the figure. When the switch is closed, the current in the circuit increases exponentially to the value i = Vemf/R. If the inductor in this circuit is replaced with an inductor having three times the number of turns per unit length, the time required to reach a current of magnitude 0.9i...a) increases.b) decreases.c) stays the same. Get solution
7mcq. Which of the following statements regarding self-induction is correct?a) Self-induction occurs only when a direct current is flowing through a circuit.b) Self-induction occurs only when an alternating current is flowing through a circuit.c) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit.d) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying. Get solution
8cc. A long solenoid has a circular cross section of radius r = 8.10 cm, a length ... = 0.540 m, and n = 2.00 · 104 turns/m. The solenoid stores 42.5 mJ of energy when it carries a current i. If the current is doubled, to 2i, the energy stored in the solenoida) decreases by a factor of 4.b) decreases by a factor of 2.c) remains the same.d) increases by a factor of 2.e) increases by a factor of 4. Get solution
8mcq. You have a light bulb, a bar magnet, a spool of wire that you can cut into as many pieces as you want, and nothing else. How can you get the bulb to light up?a) You can’t. The bulb needs electricity to light it, not magnetism.b) You cut a length of wire, connect the light bulb to the two ends of the wire, and pass the magnet through the loop that is formed.c) You cut two lengths of wire and connect the magnet and the bulb in series. Get solution
9mcq. Calculate the potential difference induced between the tips of the wings of a Boeing 747-400 with a wingspan of 64.67 m when it is in level flight at a speed of 913 km/h. Assume that the magnitude of the downward component of the Earth’s magnetic field is B = 5.00 · 10–5 T.a) 0.820 Vb) 2.95 Vc) 10.4 Vd) 30.1 Ve) 225 V Get solution
10mcq. A long solenoid with a circular cross section of radius r1 = 2.80 cm and n = 290 turns/cm is inside of and coaxial with a short coil that has a circular cross section of radius r2 = 4.90 cm and N = 31 turns. Suppose the current in the short coil is increased steadily from zero to i = 2.80 A in 18.0 ms. What is the magnitude of the potential difference induced in the solenoid while the current in the short coil is changing?a) 0.0991 Vb) 0.128 Vc) 0.233 Vd) 0.433 Ve) 0.750 V Get solution
11mcq. A long solenoid has a circular cross section of radius r = 8.10 cm, a length l = 0.540 m, and n = 2.00·104 turns/m. The solenoid is carrying a current of magnitude i = 4.04·10–3 A. How much energy is stored in the magnetic field of the solenoid?a) 2.11·10–7 Jb) 8.91·10–6 Jc) 4.57·10–5 Jd) 6.66·10–3 Je) 4.55·10–1 J Get solution
12mcq. Suppose the current in the short coil in Solved Problem 29.2 is increased steadily from zero to i = 2.80 A in 18.0 ms. What is the magnitude of the potential difference induced in the solenoid while the current in the short coil is changing?a) 0.0991 Vb) 0.128 Vc) 0.233 Vd) 0.433 Ve) 0.750 V Get solution
13mcq. Suppose the length of the rotating rod in Solved Problem 29.1 is increased by a factor of 2. By what factor does the power dissipated in the resistor change?a) ½b) 2c) 4d) 8e) 16 Get solution
14mcq. Suppose the resistance of the resistor in Solved Problem 29.1 is increased by a factor of 2. By what factor does the power dissipated in the resistor change?a) ½b) 2c) 4d) 8e) 16 Get solution
16cq. People with pacemakers or other mechanical devices as implants are often warned to stay away from large machinery or motors. Why? Get solution
17cq. Chapter 14 discussed damped harmonic oscillators, in which the damping force is velocity dependent and always opposes the motion of the oscillator. One way of producing this type of force is to use a piece of metal, such as aluminum, that moves through a nonuniform magnetic field. Explain why this technique is capable of producing a damping force. Get solution
18cq. In a popular lecture demonstration, a cylindrical permanent magnet is dropped down a long aluminum tube as shown in the figure. Neglecting friction of the magnet against the inner walls of the tube and assuming that the tube is very long compared to the size of the magnet, will the magnet accelerate downward with an acceleration equal to g (free fall)? If not, describe the eventual motion of the magnet. Does it matter if the north pole or south pole of the magnet is on the lower side?... Get solution
19cq. A popular demonstration of eddy currents involves dropping a magnet down a long metal tube and a long glass or plastic tube. As the magnet falls through a tube, the magnetic flux changes as the magnet moves toward or away from each part of the tube.a) Which tube has the larger voltage induced in it?b) Which tube has the larger eddy currents induced in it? Get solution
20cq. The current in a very long, tightly wound solenoid with radius a and n turns per unit length varies over time according to the equation i(t) = Ct2, where the current i is in amps and the time t is in seconds, and C is a constant with appropriate units. Concentric with the solenoid is a conducting ring of radius r, as shown in the figure.a) Write an expression for the potential difference induced in the ring.b) Write an expression for the magnitude of the electric field induced at n arbitrary point on the ring.c) Is the ring necessary for the induced electric field to exist?... Get solution
21cq. A circular wire ring experiences an increasing magnetic field in the upward direction, as shown in the figure. What is the direction of the induced current in the ring?... Get solution
22cq. A square conducting loop with sides of length L is rotating at a constant angular speed, ω, in a uniform magnetic field of magnitude B. At time t = 0, the loop is oriented so that the direction normal to the loop is aligned with the magnetic field. Find an expression for the potential difference induced in the loop as a function of time. Get solution
23cq. A solid metal disk of radius R is rotating around its center axis at a constant angular speed of ω. The disk is in a uniform magnetic field of magnitude B that is oriented normal to the surface of the disk. Calculate the magnitude of the potential difference between the center of the disk and the outside edge. Get solution
24cq. Large electric fields are certainly a hazard to the human body, as they can produce dangerous currents, but what about large magnetic fields? A man 1.80 m tall walks at 2.00 m/s perpendicular to a horizontal magnetic field of 5.0 T; that is, he walks between the pole faces of a very big magnet. (Such a magnet can, for example, be found in the National Superconducting Cyclotron Laboratory at Michigan State University.) Given that his body is full of conducting fluids, estimate the potential difference induced between his head and feet. Get solution
25cq. At Los Alamos National Laboratories, one means of producing very large magnetic fields is the EPFCG (explosively-pumped flux compression generator), which is used to study the effects of a high-power electromagnetic pulse (EMP) in electronic warfare. Explosives are packed and detonated in the space between a solenoid and a small copper cylinder coaxial with and inside the solenoid, as shown in the figure. The explosion occurs in a very short time and collapses the cylinder rapidly. This rapid change creates inductive currents that keep the magnetic flux constant while the cylinder’s radius shrinks by a factor of ri/rf. Estimate the magnetic field produced, assuming that the radius is compressed by a factor of 14 and the initial magnitude of the magnetic field, Bi, is 1.0 T.... Get solution
26cq. A metal hoop is laid flat on the ground. A magnetic field that is directed upward, out of the ground, is increasing in magnitude. As you look down on the hoop from above, what is the direction of the induced current in the hoop? Get solution
27cq. The wire of a tightly wound solenoid is unwound and then rewound to form another solenoid with double the diameter of the first solenoid. By what factor will the inductance change? Get solution
28. A circular coil of wire with 20 turns and a radius of 40.0 cm is laying flat on a horizontal tabletop as shown in the figure. There is a uniform magnetic field extending over the entire table with a magnitude of 5.00 T and directed to the north and downward, making an angle of 25.8° with the horizontal. What is the magnitude of the magnetic flux through the coil?... Get solution
29. When a magnet in an MRI is abruptly shut down, the magnet is said to be quenched. Quenching can occur in as little as 20.0 s. Suppose a magnet with an initial field of 1.20 T is quenched in 20.0 s, and the final field is approximately zero. Under these conditions, what is the average induced potential difference around a conducting loop of radius 1.00 cm (about the size of a wedding ring) oriented perpendicular to the field? Get solution
30. An 8-turn coil has square loops measuring 0.200 m along a side and a resistance of 3.00 Ω. It is placed in a magnetic field that makes an angle of 40.0° with the plane of each loop. The magnitude of this field varies with time according to B = 1.50t3, where t is measured in seconds and B in teslas. What is the induced current in the coil at t = 2.00 s? Get solution
31. A metal loop has an area of 0.100 m2 and is placed flat on the ground. There is a uniform magnetic field pointing due west, as shown in the figure. This magnetic field initially has a magnitude of 0.123 T, which decreases steadily to 0.075 T during a period of 0.579 s. Find the potential difference induced in the loop during this time.... Get solution
32. A respiration monitor has a flexible loop of copper wire, which wraps about the chest. As the wearer breathes, the radius of the loop of wire increases and decreases. When a person in the Earth’s magnetic field (assume 0.426 · 10–4 T) inhales, what is the average current in the loop, assuming that it has a resistance of 30.0 Ω and increases in radius from 20.0 cm to 25.0 cm over 1.00 s? Assume that the magnetic field is perpendicular to the plane of the loop. Get solution
33. A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b >> a (b much greater than a) and resistance R1. A time-dependent voltage is applied to the larger loop; its slow sinusoidal variation in time is given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop.... Get solution
34. A long solenid with cross-sectional area A1 surrounds another long solenoid with cross-sectional area A2 A1 and resistance R. Both solenoids have the same length and the same number of turns. A current given by i = i0 cos ωt is flowing through the outer solenoid. Find an expression for the magnetic field in the inner solenoid due to the induced current. Get solution
35. The conducting loop in the shape of a quarter-circle shown in the figure has a radius of 10.0 cm and a resistance of 0.200 Ω. The magnetic field strength within the dotted circle of radius 3.00 cm is initially 2.00 T. The magnetic field strength then decreases from 2.00 T to 1.00 T in 2.00 s. Find (a) the magnitude and (b) the direction of the induced current in the loop.... Get solution
36. A supersonic aircraft with a wingspan of 10.0 m is flying over the north magnetic pole (in a magnetic field of magnitude 0.500 G oriented perpendicular to the ground) at a speed of three times the speed of sound (Mach 3). What is the potential difference between the tips of the wings? Assume that the wings are made of aluminum. Get solution
37. A helicopter hovers above the north magnetic pole in a magnetic field of magnitude 0.426 G and oriented perpendicular to the ground. The helicopter rotors are 10.0 m long, are made of aluminum, and rotate about the hub with a rotational speed of 1.00 · 104 rpm. What is the potential difference from the hub to the end of a rotor ? Get solution
38. An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.100 m and v = 0.0150 m/s. The loop has a constant resistance of R = 12.0 Ω and is placed in a uniform magnetic field of magnitude B0 = 0.750 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 5.00 s.... Get solution
39. A rectangular frame of conducting wire has negligible resistance and width w and is held vertically in a magnetic field of magnitude B, as shown in the figure. A metal bar with mass m and resistance R is placed across the frame, maintaining contact with the frame. Derive an expression for the terminal velocity of the bar if it is allowed to fall freely along this frame starting from rest. Neglect friction between the wires and the metal bar.... Get solution
40. Two parallel conducting rails with negligible resistance are connected at one end by a resistor of resistance R, as shown in the figure. The rails are placed in a magnetic field... which is perpendicular to the plane of the rails. This magnetic field is uniform and time independent. The distance between the rails is .... A conducting rod slides without friction on top of the two rails at constant velocity....a) Using Faraday’s Law of Induction, calculate the magnitude of the potential difference induced in the moving rod.b) Calculate the magnitude of the induced current in the rod, iind.c) Show that for the rod to move at a constant velocity as shown, it must be pulled with an external force, ... , and calculate the magnitude of this force.d) Calculate the work done, Wext, and the power generated, Pext, by the external force in moving the rod.e) Calculate the power used (dissipated) by the resistor, PR. Explain the correlation between this result and those of part (d)....... Get solution
41. A long, straight wire runs along the y-axis. The wire carries a current in the positive y-direction that is changing as a function of time according to i = 2.00 A + (0.300 A/s)t. A loop of wire is located in the xy-plane near the y-axis, as shown in the figure. The loop has dimensions 7.00 m by 5.00 m and is 1.00 m away from the wire. What is the induced potential difference in the wire loop at t = 10.0 s?... Get solution
42. The long, straight wire in the figure has a current i = 1.00 A flowing in it. A square loop with 10.0-cm sides and a resistance of 0.0200 Ω is positioned 10.0 cm away from the wire. The loop is then moved in the positive x-direction with a speed v = 10.0 cm/s.a) Find the direction of the induced current in the loop.b) Identify the directions of the magnetic forces acting on all sides of the square loop.c) Calculate the direction and the magnitude of the net force acting on the loop at the instant it starts to move.... Get solution
43. A simple generator consists of a loop rotating inside a constant magnetic field (see Figure 29.19). If the loop is rotating with frequency f, the magnetic flux is given by Φ(t) = BA cos (2πft). If B = 1.00 T and A = 1.00 m2, what must the value of f be for the maximum induced potential difference to be 110. V?Figure 29.19 (a) A simple direct-current (DC) generator/motor. (b) A simple alternating-current (AC) generator/motor.... ... Get solution
44. A motor has a single loop inside a magnetic field of magnitude 0.870 T. If the area of the loop is 300. cm2, find the maximum angular speed possible for this motor when connected to a source of emf providing 170. V. Get solution
45. Your friend decides to produce electrical power by turning a coil of 1.00 · 105 circular loops of wire around an axis perpendicular to the Earth’s magnetic field, which has a local magnitude of 0.300 G. The loops have a radius of 25.0 cm.a) If your friend turns the coil at a frequency of 150. Hz, what peak current will flow in a resistor, R = 1.50 kΩ, connected to the coil?b) The average current flowing in the coil will be 0.7071 times the peak current. What will be the average power obtained from this device? Get solution
46. Find the mutual inductance of the solenoid and the coil described in Example 29.1 and the induced potential difference in the coil at t = 2.0 s using the techniques described in Section 29.7. How do the results for the induced potential difference compare?Example 29.1 Potential Difference Induced by a Changing Magnetic Field......... Get solution
47. The figure shows the current through a 10.0-Mh inductor over a time interval of 8.00 ms. Draw a graph showing the self-induced potential difference, ∆Vind,L, for the inductor over the same interval.... Get solution
48. A short coil with radius R = 10.0 cm contains N = 30.0 turns and surrounds a long solenoid with radius r = 8.00 cm containing n = 60 turns per centimeter. The current in the short coil is increased at a constant rate from zero to i = 2.00 A in a time of t = 12.0 s. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil. Get solution
49. Consider an RL circuit with resistance R = 1.00 MΩ and inductance L = 1.00 H, which is powered by a 10.0-V battery.a) What is the time constant of the circuit?b) If the switch is closed at time t = 0, what is the current just after that time? After 2.00 µs? When a long time has passed? Get solution
50. In the circuit in the figure, R = 120. Ω, L = 3.00 H, and Vemf = 40.0 V. After the switch is closed, how long will it take the current in the inductor to reach 300. mA?... Get solution
51. The current is increasing at a rate of 3.60 A/s in an RL circuit with R = 3.25 Ω and L = 440. mH. What is the potential difference across the circuit at the moment when the current in the circuit is 3.00 A? Get solution
52. In the circuit in the figure, a battery supplies Vemf = 18.0 V and R1 = 6.00 Ω, R2 = 6.00 Ω, and L = 5.00 H. Calculate each of the following immediately after the switch is closed:a) the current flowing out of the batteryb) the current through R1c) the current through R2d) the potential difference across R1e) the potential difference across R2f) the potential difference across Lg) the rate of current change across R1... Get solution
53. In the circuit in the figure, a battery supplies Vemf = 18.0 V and R1 = 6.00 Ω, R2 = 6.00 Ω, and L = 5.00 H. Calculate each of the following a long time after the switch is closed:a) the current flowing out of the batteryb) the current through R1c) the current through R2d) the potential difference across R1e) the potential difference across R2f) the potential difference across Lg) the rate of current change across R1... Get solution
54. A circuit contains a battery, three resistors, and an inductor, as shown in the figure. What will be the current through each resistor (a) immediately after the switch is closed and (b) a long time after the witch is closed? (c) Suppose the switch is reopened a long time after it has been closed. What is the current in each resistor? After a long time?... Get solution
55. Having just learned that there is energy associated with magnetic fields, an inventor sets out to tap the energy associated with the Earth’s magnetic field. What volume of space near Earth’s surface contains 1.00 J of energy, assuming the strength of the magnetic field to be 5.00 · 10–5 T? Get solution
56. A clinical MRI (magnetic resonance imaging) superconducting magnet can be approximated as a solenoid with a diameter of 1.00 m, a length of 1.50 m, and a uniform magnetic field of 3.00 T. Determine (a) the energy density of the magnetic field and (b) the total energy in the solenoid.... Get solution
57. A magnetar (magnetic neutron star) has a magnetic field near its surface of magnitude 4.00 · 1010 T.a) Calculate the energy density of this magnetic field.b) The Special Theory of Relativity associates energy with any mass m at rest according to E0 = mc2 (more on this in Chapter 35). Find the rest mass density associated with the energy density of part (a). Get solution
58. An emf of 20.0 V is applied to a coil with an inductance of 40.0 mH and a resistance of 0.500 Ω.a) Determine the energy stored in the magnetic field when the current reaches ¼ of its maximum value.b) How long does it take for the current to reach this value? Get solution
59. A student wearing a 15.0-g gold band with radius 0.750 cm (and with a resistance of 61.9 µΩ and a specific heat capacity of c = 129 J/kg °C) on her finger moves her finger from a region having a magnetic field of 0.0800 T, pointing along her finger, to a region with zero magnetic field in 40.0 ms. As a result of this action, thermal energy is added to the band due to the induced current, which raises the temperature of the band. Calculate the temperature rise in the band, assuming that all the energy produced is used in raising the temperature. Get solution
60. A coil with N turns and area A, carrying a constant current, i, flips in an external magnetic field, ... so that its dipole moment switches from induction produces a potential difference that tends to reduce the current in the coil. Calculate the work done by the coil’s power supply to maintain the constant current. Get solution
61. An electromagnetic wave propagating in vacuum has electric and magnetic fields given by ... and ... where ... is given by ... and the wave vector ... is perpendicular to both ... and .... The magnitude of ... and the angular frequency ω satisfy the dispersion relation, ... where µ0 and ε0 are the permeability and permittivity of free space, respectively. Such a wave transports energy in both its electric and magnetic fields. Calculate the ratio of the energy densities of the magnetic and electric fields, uB/uE, in this wave. Simplify your final answer as much as possible. Get solution
62. A wire of length ... = 10.0 cm is moving with constant velocity in the xy-plane; the wire is parallel to the y-axis and moving along the x-axis. If a magnetic field of magnitude 1.00 T is pointing along the positive z-axis, what must the velocity of the wire be in order for a potential difference of 2.00 V to be induced across it? Get solution
63. The magnetic field inside the solenoid in the figure changes at the rate of 1.50 T/s. A conducting coil with 2000 turns surrounds the solenoid, as shown. The radius of the solenoid is 4.00 cm, and the radius of the coil is 7.00 cm. What is the potential difference induced in the coil?... Get solution
64. An ideal battery (with no internal resistance) supplies Vemf and is connected to a superconducting (no resistance!) coil of inductance L at time t = 0. Find the current in the coil as a function of time, i(t). Assume that all connections also have zero resistance. Get solution
65. A 100-turn solenoid of length 8.00 cm and radius 6.00 mm carries a current of 0.400 A from right to left. The current is then reversed so that it flows from left to right. By how much does the energy stored in the magnetic field inside the solenoid change? Get solution
66. The electric field near the Earth’s surface has a magnitude of 150. N/C, and the magnitude of the Earth’s magnetic field near the surface is typically 50.0 µT. Calculate and compare the energy densities associated with these two fields. Assume that the electric and magnetic properties of air are essentially those of a vacuum. Get solution
67. What is the inductance in a series RL circuit in which R = 3.00 kΩ if the current increases to ½ of its final value in 20.0 µs? Get solution
68. A 100.-V battery is connected in series with a 500.-Ω resistor. According to Faraday’s Law of Induction, current can never change instantaneously, so there is always some “stray” inductance. Suppose the stray inductance is 0.200 µH. How long will it take the current to build up to within 0.500% of its final value of 0.200 A after the resistor is connected to the battery? Get solution
69. A single loop of wire with an area of 5.00 m2 is located in the plane of the page, as shown in the figure. A time-varying magnetic field in the region of the loop is directed into the page, and its magnitude is given by B = 3.00 T + (2.00 T/s)t. At t = 2.00 s, what are the induced potential difference in the loop and the direction of the induced current?... Get solution
70. A 9.00-V battery is connected through a switch to two identical resistors and an ideal inductor, as shown in the figure. Each of the resistors has a resistance of 100. Ω, and the inductor has an inductance of 3.00 H. The switch is initially open.a) Immediately after the switch is closed, what is the current in resistor R1 and in resistor R2?b) At 50.0 ms after the switch is closed, what is the current in resistor R1 and in resistor R2?c) At 500. ms after the switch is closed, what is the current in resistor R1 and in resistor R2?d) After a long time (> 10.0 s), the switch is opened again. Immediately after the switch is opened, what is the current in resistor R1 and in resistor R2?e) At 50.0 ms after the switch is opened, what is the current in resistor R1 and in resistor R2?f) At 500. ms after the switch is opened, what is the current in resistor R1 and in resistor R2?... Get solution
71. A long solenoid with length 3.00 m and n = 290. turns/m carries a current of 3.00 A. It stores 2.80 J of energy. What is the cross-sectional area of the solenoid? Get solution
72. A rectangular conducting loop with dimensions a and b and resistance R is placed in the xy-plane. A magnetic field of magnitude B passes through the loop. The magnetic field is in the positive z-direction and varies in time according to B = B0(1 + c1t3), where c1 is a constant with units of 1/s3. What is the direction of the current induced in the loop, and what is its value at t = 1 s (in terms of a, b, R, B0, and c1)? Get solution
73. A circuit contains a 12.0-V battery, a switch, and a light bulb connected in series. When the light bulb has a current of 0.100 A flowing in it, it just starts to glow. This bulb draws 2.00 W when the switch has been closed for a long time. The switch is opened, and an inductor is added to the circuit, in series with the bulb. If the light bulb begins to glow 3.50 ms after the switch is closed again, what is the magnitude of the inductance? Ignore any time needed to heat the filament, and assume that you are able to observe a glow as soon as the current in the filament reaches the 0.100-A threshold. Get solution
74. A circular loop of area A is placed perpendicular to a time-varying magnetic field of magnitude B(t) = B0 + at + bt2, where B0, a, and b are constants.a) What is the magnetic flux through the loop at t = 0?b) Derive an equation for the induced potential difference in the loop as a function of time.c) What are the magnitude and the direction of the induced current if the resistance of the loop is R? Get solution
75. A conducting rod of length 50.0 cm slides over two parallel metal bars placed in a magnetic field with a magnitude of 1.00 kG, as shown in the figure. The ends of the rods are connected by two resistors, R1 = 100. Ω and R2 = 200. Ω. The conducting rod moves with a constant speed of 8.00 m/s.a) What are the currents flowing through the two resistors?b) What power is delivered to the resistors?c) What force is needed to keep the rod moving with constant velocity?... Get solution
76. A rectangular wire loop (dimensions of h = 15.0 cm and w = 8.00 cm) with resistance R = 5.00 Ω is mounted on a door, as shown in the figure. The Earth’s magnetic field, BE = 2.60 · 10–5 T, is uniform and perpendicular to the surface of the closed door (the surface is in the xz-plane). At time t = 0, the door is opened (right edge moves toward the y-axis) at a constant rate, with an opening angle of θ(t) = ωt, where ω = 3.50 rad/s. Calculate the direction and the magnitude of the current induced in the loop, i(t = 0.200 s)....... Get solution
77. A steel cylinder with radius 2.50 cm and length 10.0 cm rolls without slipping down a ramp that is inclined at 15.0° above the horizontal and has a length (along the ramp) of 3.00 m. What is the induced potential difference between the ends of the cylinder as the cylinder leaves the bottom of the ramp, if the downward slope of the ramp points in the direction of the Earth’s magnetic field at that location? (Use 0.426 G for the local strength of the Earth’s magnetic field.) Get solution
78. The figure shows a circuit in which a battery is connected to a resistor and an inductor in series.a) What is the current in the circuit at any time t after the switch is closed?b) Calculate the total energy provided by the battery from t = 0 to t = L/R.c) Calculate the total energy dissipated in the resistor over the same time period.d) Is energy conserved in this circuit?... Get solution
79. As shown in the figure, a rectangular (60.0 cm long by 15.0 cm wide) circuit loop with resistance 35.0 Ω is held parallel to the xy-plane with one half inside a uniform magnetic field. A magnetic field given by ... = 2.00ẑ T is directed along the positive z-axis to the right of the dashed line; there is no external magnetic field to the left of the dashed line.a) Calculate the magnitude of the force required to move the loop to the left at a constant speed of 10.0 cm/s while the right end of the loop is still in the magnetic field.b) What power is expended to pull the loop out of the magnetic field at this speed?c) What is the power dissipated by the resistor?... Get solution
81. What is the inductance in an RL circuit with R = 17.88 Ω if the time required for the current to reach 75% of its maximum value is 3.450 ms? Get solution
82. For an RL circuit with R = 21.84 Ω and L = 55.93 mH, how long does it take the current to reach 75% of its maximum value? Get solution
83. A wedding ring (of diameter 1.95 cm) is tossed into the air and given a spin, resulting in an angular velocity of 13.3 rev/s. The rotation axis is a diameter of the ring. If the magnitude of the Earth’s magnetic field at the ring’s location is 4.77 · 10–5 T, what is the maximum induced potential difference in the ring? Get solution
84. A wedding ring is tossed into the air and given a spin, resulting in an angular velocity of 13.5 rev/s. The rotation axis is a diameter of the ring. .The magnitude of the Earth’s magnetic field is 4.97 · 10–5 T at the ring’s location. If the maximum induced voltage in the ring is 1.446 · 10–6 V, what is the diameter of the ring? Get solution
85. A wedding ring of diameter 1.63 cm is tossed into the air and given a spin, resulting in an angular velocity of 13.7 rev/s. The rotation axis is a diameter of the ring. If the maximum induced voltage in the ring is 6.556 · 10–7 V, what is the magnitude of the Earth’s magnetic field at this location? Get solution
1mcq. A solenoid with 200 turns and a cross-sectional area of 60 cm2 has a magnetic field of 0.60 T along its axis. If the field is confined within the solenoid and changes at a rate of 0.20 T/s, the magnitude of the induced potential difference in the solenoid will bea) 0.0020 V.b) 0.02 V.c) 0.001 V.d) 0.24 V. Get solution
2cc. A power supply is connected to loop 1 and an ammeter as shown in the figure. Loop 2 is close to loop 1 and is connected to a voltmeter. A graph of the current i through loop 1 as a function of time, t, is also shown in the figure. Which graph best describes the induced potential difference, ΔVind, in loop 2 as a function of time, t?...Graph 1...Graph 2...Graph 3...Graph 4...a) graph 1b) graph 2c) graph 3d) graph 4 Get solution
2mcq. The rectangular loop of wire in Figure 29.9 is pulled with a constant acceleration from a region of zero magnetic field into a region of a uniform magnetic field. During this process, the current induced in the loopa) will be zero.b) will be some constant value that is not zero.c) will increase linearly with time.d) will increase exponentially with time.e) will increase linearly with the square of the time.Figure 29.9 A wire loop (blue) is pulled out of a gap between two magnets... Get solution
3cc. A long wire carries a current, i, as shown in the figure. A square loop moves in the same plane as the wire, as indicated. In which cases will the loop have an induced current?Case 1...Case 2...Case 3...a) cases 1 and 2b) cases 1 and 3c) cases 2 and 3d) None of the loops will have an induced current.e) All of the loops will have an induced current. Get solution
3mcq. Which of the following will induce a current in a loop of wire in a uniform magnetic field?a) decreasing the strength of the fieldb) rotating the loop about an axis parallel to the fieldc) moving the loop within the fieldd) all of the abovee) none of the above Get solution
4cc. A metal bar is moving with constant velocity ... through a uniform magnetic field pointing into the page, as shown in the figure. Which of the following most accurately represents the charge distribution on the surface of the metal bar?...Distribution1...Distribution2...Distribution3...Distribution4...Distribution5...a) distribution 1b) distribution 2c) distribution 3d) distribution 4e) distribution 5 Get solution
4mcq. Faraday’s Law of Induction states thata) a potential difference is induced in a loop when there is a change in the magnetic flux through the loop.b) the current induced in a loop by a changing magnetic field produces a magnetic field that opposes this change in magnetic field.c) a changing magnetic field induces an electric field.d) the inductance of a device is a measure of its opposition to changes in current flowing through it.e) magnetic flux is the product of the average magnetic field and the area perpendicular to it that it penetrates. Get solution
5cc. A wire loop is placed in a uniform magnetic field. Over a period of 2 s, the loop is shrunk. Which statement about the induced potential difference is correct?...a) There will be some induced potential difference.b) There will be no induced potential difference because the loop changes size along one axis and not the other.c) There will be no induced potential difference because the loop is not closed.d) There will be no induced potential difference because the loop is shrinking. Get solution
5mcq. A conducting ring is moving from left to right through a uniform magnetic field, as shown in the figure. In which region(s) is there an induced current in the ring?...a) regions B and Db) regions B, C, and Dc) region Cd) regions A through E Get solution
6cc. Two identical coils are shown in the figure. Coil 1 has a current i flowing in the direction shown. When the switch in the circuit containing coil 1 is opened, what happens in coil 2?Coil 1...Coil 2...a) A current is induced in coil 2 that flows in direction 1.b) A current is induced in coil 2 that flows in direction 2.c) No current is induced in coil 2. Get solution
6mcq. A circular loop of wire moving in the xy-plane with a constant velocity in the negative x-direction enters a uniform magnetic field, which covers the region in which x ...a) The induced potential difference in the loop is at a maximum as the edge of the loop just enters the region with the magnetic field.b) The induced potential difference in the loop is at a maximum when one fourth of the loop is in the region with the magnetic field.c) The induced potential difference in the loop is at a maximum when the loop is halfway into the region with the magnetic field.d) The induced potential difference in the loop is constant from the instant the loop starts to enter the region with the magnetic field. Get solution
7cc. Consider the RL circuit shown in the figure. When the switch is closed, the current in the circuit increases exponentially to the value i = Vemf/R. If the inductor in this circuit is replaced with an inductor having three times the number of turns per unit length, the time required to reach a current of magnitude 0.9i...a) increases.b) decreases.c) stays the same. Get solution
7mcq. Which of the following statements regarding self-induction is correct?a) Self-induction occurs only when a direct current is flowing through a circuit.b) Self-induction occurs only when an alternating current is flowing through a circuit.c) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit.d) Self-induction occurs when either a direct current or an alternating current is flowing through a circuit as long as the current is varying. Get solution
8cc. A long solenoid has a circular cross section of radius r = 8.10 cm, a length ... = 0.540 m, and n = 2.00 · 104 turns/m. The solenoid stores 42.5 mJ of energy when it carries a current i. If the current is doubled, to 2i, the energy stored in the solenoida) decreases by a factor of 4.b) decreases by a factor of 2.c) remains the same.d) increases by a factor of 2.e) increases by a factor of 4. Get solution
8mcq. You have a light bulb, a bar magnet, a spool of wire that you can cut into as many pieces as you want, and nothing else. How can you get the bulb to light up?a) You can’t. The bulb needs electricity to light it, not magnetism.b) You cut a length of wire, connect the light bulb to the two ends of the wire, and pass the magnet through the loop that is formed.c) You cut two lengths of wire and connect the magnet and the bulb in series. Get solution
9mcq. Calculate the potential difference induced between the tips of the wings of a Boeing 747-400 with a wingspan of 64.67 m when it is in level flight at a speed of 913 km/h. Assume that the magnitude of the downward component of the Earth’s magnetic field is B = 5.00 · 10–5 T.a) 0.820 Vb) 2.95 Vc) 10.4 Vd) 30.1 Ve) 225 V Get solution
10mcq. A long solenoid with a circular cross section of radius r1 = 2.80 cm and n = 290 turns/cm is inside of and coaxial with a short coil that has a circular cross section of radius r2 = 4.90 cm and N = 31 turns. Suppose the current in the short coil is increased steadily from zero to i = 2.80 A in 18.0 ms. What is the magnitude of the potential difference induced in the solenoid while the current in the short coil is changing?a) 0.0991 Vb) 0.128 Vc) 0.233 Vd) 0.433 Ve) 0.750 V Get solution
11mcq. A long solenoid has a circular cross section of radius r = 8.10 cm, a length l = 0.540 m, and n = 2.00·104 turns/m. The solenoid is carrying a current of magnitude i = 4.04·10–3 A. How much energy is stored in the magnetic field of the solenoid?a) 2.11·10–7 Jb) 8.91·10–6 Jc) 4.57·10–5 Jd) 6.66·10–3 Je) 4.55·10–1 J Get solution
12mcq. Suppose the current in the short coil in Solved Problem 29.2 is increased steadily from zero to i = 2.80 A in 18.0 ms. What is the magnitude of the potential difference induced in the solenoid while the current in the short coil is changing?a) 0.0991 Vb) 0.128 Vc) 0.233 Vd) 0.433 Ve) 0.750 V Get solution
13mcq. Suppose the length of the rotating rod in Solved Problem 29.1 is increased by a factor of 2. By what factor does the power dissipated in the resistor change?a) ½b) 2c) 4d) 8e) 16 Get solution
14mcq. Suppose the resistance of the resistor in Solved Problem 29.1 is increased by a factor of 2. By what factor does the power dissipated in the resistor change?a) ½b) 2c) 4d) 8e) 16 Get solution
16cq. People with pacemakers or other mechanical devices as implants are often warned to stay away from large machinery or motors. Why? Get solution
17cq. Chapter 14 discussed damped harmonic oscillators, in which the damping force is velocity dependent and always opposes the motion of the oscillator. One way of producing this type of force is to use a piece of metal, such as aluminum, that moves through a nonuniform magnetic field. Explain why this technique is capable of producing a damping force. Get solution
18cq. In a popular lecture demonstration, a cylindrical permanent magnet is dropped down a long aluminum tube as shown in the figure. Neglecting friction of the magnet against the inner walls of the tube and assuming that the tube is very long compared to the size of the magnet, will the magnet accelerate downward with an acceleration equal to g (free fall)? If not, describe the eventual motion of the magnet. Does it matter if the north pole or south pole of the magnet is on the lower side?... Get solution
19cq. A popular demonstration of eddy currents involves dropping a magnet down a long metal tube and a long glass or plastic tube. As the magnet falls through a tube, the magnetic flux changes as the magnet moves toward or away from each part of the tube.a) Which tube has the larger voltage induced in it?b) Which tube has the larger eddy currents induced in it? Get solution
20cq. The current in a very long, tightly wound solenoid with radius a and n turns per unit length varies over time according to the equation i(t) = Ct2, where the current i is in amps and the time t is in seconds, and C is a constant with appropriate units. Concentric with the solenoid is a conducting ring of radius r, as shown in the figure.a) Write an expression for the potential difference induced in the ring.b) Write an expression for the magnitude of the electric field induced at n arbitrary point on the ring.c) Is the ring necessary for the induced electric field to exist?... Get solution
21cq. A circular wire ring experiences an increasing magnetic field in the upward direction, as shown in the figure. What is the direction of the induced current in the ring?... Get solution
22cq. A square conducting loop with sides of length L is rotating at a constant angular speed, ω, in a uniform magnetic field of magnitude B. At time t = 0, the loop is oriented so that the direction normal to the loop is aligned with the magnetic field. Find an expression for the potential difference induced in the loop as a function of time. Get solution
23cq. A solid metal disk of radius R is rotating around its center axis at a constant angular speed of ω. The disk is in a uniform magnetic field of magnitude B that is oriented normal to the surface of the disk. Calculate the magnitude of the potential difference between the center of the disk and the outside edge. Get solution
24cq. Large electric fields are certainly a hazard to the human body, as they can produce dangerous currents, but what about large magnetic fields? A man 1.80 m tall walks at 2.00 m/s perpendicular to a horizontal magnetic field of 5.0 T; that is, he walks between the pole faces of a very big magnet. (Such a magnet can, for example, be found in the National Superconducting Cyclotron Laboratory at Michigan State University.) Given that his body is full of conducting fluids, estimate the potential difference induced between his head and feet. Get solution
25cq. At Los Alamos National Laboratories, one means of producing very large magnetic fields is the EPFCG (explosively-pumped flux compression generator), which is used to study the effects of a high-power electromagnetic pulse (EMP) in electronic warfare. Explosives are packed and detonated in the space between a solenoid and a small copper cylinder coaxial with and inside the solenoid, as shown in the figure. The explosion occurs in a very short time and collapses the cylinder rapidly. This rapid change creates inductive currents that keep the magnetic flux constant while the cylinder’s radius shrinks by a factor of ri/rf. Estimate the magnetic field produced, assuming that the radius is compressed by a factor of 14 and the initial magnitude of the magnetic field, Bi, is 1.0 T.... Get solution
26cq. A metal hoop is laid flat on the ground. A magnetic field that is directed upward, out of the ground, is increasing in magnitude. As you look down on the hoop from above, what is the direction of the induced current in the hoop? Get solution
27cq. The wire of a tightly wound solenoid is unwound and then rewound to form another solenoid with double the diameter of the first solenoid. By what factor will the inductance change? Get solution
28. A circular coil of wire with 20 turns and a radius of 40.0 cm is laying flat on a horizontal tabletop as shown in the figure. There is a uniform magnetic field extending over the entire table with a magnitude of 5.00 T and directed to the north and downward, making an angle of 25.8° with the horizontal. What is the magnitude of the magnetic flux through the coil?... Get solution
29. When a magnet in an MRI is abruptly shut down, the magnet is said to be quenched. Quenching can occur in as little as 20.0 s. Suppose a magnet with an initial field of 1.20 T is quenched in 20.0 s, and the final field is approximately zero. Under these conditions, what is the average induced potential difference around a conducting loop of radius 1.00 cm (about the size of a wedding ring) oriented perpendicular to the field? Get solution
30. An 8-turn coil has square loops measuring 0.200 m along a side and a resistance of 3.00 Ω. It is placed in a magnetic field that makes an angle of 40.0° with the plane of each loop. The magnitude of this field varies with time according to B = 1.50t3, where t is measured in seconds and B in teslas. What is the induced current in the coil at t = 2.00 s? Get solution
31. A metal loop has an area of 0.100 m2 and is placed flat on the ground. There is a uniform magnetic field pointing due west, as shown in the figure. This magnetic field initially has a magnitude of 0.123 T, which decreases steadily to 0.075 T during a period of 0.579 s. Find the potential difference induced in the loop during this time.... Get solution
32. A respiration monitor has a flexible loop of copper wire, which wraps about the chest. As the wearer breathes, the radius of the loop of wire increases and decreases. When a person in the Earth’s magnetic field (assume 0.426 · 10–4 T) inhales, what is the average current in the loop, assuming that it has a resistance of 30.0 Ω and increases in radius from 20.0 cm to 25.0 cm over 1.00 s? Assume that the magnetic field is perpendicular to the plane of the loop. Get solution
33. A circular conducting loop with radius a and resistance R2 is concentric with a circular conducting loop with radius b >> a (b much greater than a) and resistance R1. A time-dependent voltage is applied to the larger loop; its slow sinusoidal variation in time is given by V(t) = V0 sin ωt, where V0 and ω are constants with dimensions of voltage and inverse time, respectively. Assuming that the magnetic field throughout the inner loop is uniform (constant in space) and equal to the field at the center of the loop, derive expressions for the potential difference induced in the inner loop and the current i through that loop.... Get solution
34. A long solenid with cross-sectional area A1 surrounds another long solenoid with cross-sectional area A2 A1 and resistance R. Both solenoids have the same length and the same number of turns. A current given by i = i0 cos ωt is flowing through the outer solenoid. Find an expression for the magnetic field in the inner solenoid due to the induced current. Get solution
35. The conducting loop in the shape of a quarter-circle shown in the figure has a radius of 10.0 cm and a resistance of 0.200 Ω. The magnetic field strength within the dotted circle of radius 3.00 cm is initially 2.00 T. The magnetic field strength then decreases from 2.00 T to 1.00 T in 2.00 s. Find (a) the magnitude and (b) the direction of the induced current in the loop.... Get solution
36. A supersonic aircraft with a wingspan of 10.0 m is flying over the north magnetic pole (in a magnetic field of magnitude 0.500 G oriented perpendicular to the ground) at a speed of three times the speed of sound (Mach 3). What is the potential difference between the tips of the wings? Assume that the wings are made of aluminum. Get solution
37. A helicopter hovers above the north magnetic pole in a magnetic field of magnitude 0.426 G and oriented perpendicular to the ground. The helicopter rotors are 10.0 m long, are made of aluminum, and rotate about the hub with a rotational speed of 1.00 · 104 rpm. What is the potential difference from the hub to the end of a rotor ? Get solution
38. An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.100 m and v = 0.0150 m/s. The loop has a constant resistance of R = 12.0 Ω and is placed in a uniform magnetic field of magnitude B0 = 0.750 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 5.00 s.... Get solution
39. A rectangular frame of conducting wire has negligible resistance and width w and is held vertically in a magnetic field of magnitude B, as shown in the figure. A metal bar with mass m and resistance R is placed across the frame, maintaining contact with the frame. Derive an expression for the terminal velocity of the bar if it is allowed to fall freely along this frame starting from rest. Neglect friction between the wires and the metal bar.... Get solution
40. Two parallel conducting rails with negligible resistance are connected at one end by a resistor of resistance R, as shown in the figure. The rails are placed in a magnetic field... which is perpendicular to the plane of the rails. This magnetic field is uniform and time independent. The distance between the rails is .... A conducting rod slides without friction on top of the two rails at constant velocity....a) Using Faraday’s Law of Induction, calculate the magnitude of the potential difference induced in the moving rod.b) Calculate the magnitude of the induced current in the rod, iind.c) Show that for the rod to move at a constant velocity as shown, it must be pulled with an external force, ... , and calculate the magnitude of this force.d) Calculate the work done, Wext, and the power generated, Pext, by the external force in moving the rod.e) Calculate the power used (dissipated) by the resistor, PR. Explain the correlation between this result and those of part (d)....... Get solution
41. A long, straight wire runs along the y-axis. The wire carries a current in the positive y-direction that is changing as a function of time according to i = 2.00 A + (0.300 A/s)t. A loop of wire is located in the xy-plane near the y-axis, as shown in the figure. The loop has dimensions 7.00 m by 5.00 m and is 1.00 m away from the wire. What is the induced potential difference in the wire loop at t = 10.0 s?... Get solution
42. The long, straight wire in the figure has a current i = 1.00 A flowing in it. A square loop with 10.0-cm sides and a resistance of 0.0200 Ω is positioned 10.0 cm away from the wire. The loop is then moved in the positive x-direction with a speed v = 10.0 cm/s.a) Find the direction of the induced current in the loop.b) Identify the directions of the magnetic forces acting on all sides of the square loop.c) Calculate the direction and the magnitude of the net force acting on the loop at the instant it starts to move.... Get solution
43. A simple generator consists of a loop rotating inside a constant magnetic field (see Figure 29.19). If the loop is rotating with frequency f, the magnetic flux is given by Φ(t) = BA cos (2πft). If B = 1.00 T and A = 1.00 m2, what must the value of f be for the maximum induced potential difference to be 110. V?Figure 29.19 (a) A simple direct-current (DC) generator/motor. (b) A simple alternating-current (AC) generator/motor.... ... Get solution
44. A motor has a single loop inside a magnetic field of magnitude 0.870 T. If the area of the loop is 300. cm2, find the maximum angular speed possible for this motor when connected to a source of emf providing 170. V. Get solution
45. Your friend decides to produce electrical power by turning a coil of 1.00 · 105 circular loops of wire around an axis perpendicular to the Earth’s magnetic field, which has a local magnitude of 0.300 G. The loops have a radius of 25.0 cm.a) If your friend turns the coil at a frequency of 150. Hz, what peak current will flow in a resistor, R = 1.50 kΩ, connected to the coil?b) The average current flowing in the coil will be 0.7071 times the peak current. What will be the average power obtained from this device? Get solution
46. Find the mutual inductance of the solenoid and the coil described in Example 29.1 and the induced potential difference in the coil at t = 2.0 s using the techniques described in Section 29.7. How do the results for the induced potential difference compare?Example 29.1 Potential Difference Induced by a Changing Magnetic Field......... Get solution
47. The figure shows the current through a 10.0-Mh inductor over a time interval of 8.00 ms. Draw a graph showing the self-induced potential difference, ∆Vind,L, for the inductor over the same interval.... Get solution
48. A short coil with radius R = 10.0 cm contains N = 30.0 turns and surrounds a long solenoid with radius r = 8.00 cm containing n = 60 turns per centimeter. The current in the short coil is increased at a constant rate from zero to i = 2.00 A in a time of t = 12.0 s. Calculate the induced potential difference in the long solenoid while the current is increasing in the short coil. Get solution
49. Consider an RL circuit with resistance R = 1.00 MΩ and inductance L = 1.00 H, which is powered by a 10.0-V battery.a) What is the time constant of the circuit?b) If the switch is closed at time t = 0, what is the current just after that time? After 2.00 µs? When a long time has passed? Get solution
50. In the circuit in the figure, R = 120. Ω, L = 3.00 H, and Vemf = 40.0 V. After the switch is closed, how long will it take the current in the inductor to reach 300. mA?... Get solution
51. The current is increasing at a rate of 3.60 A/s in an RL circuit with R = 3.25 Ω and L = 440. mH. What is the potential difference across the circuit at the moment when the current in the circuit is 3.00 A? Get solution
52. In the circuit in the figure, a battery supplies Vemf = 18.0 V and R1 = 6.00 Ω, R2 = 6.00 Ω, and L = 5.00 H. Calculate each of the following immediately after the switch is closed:a) the current flowing out of the batteryb) the current through R1c) the current through R2d) the potential difference across R1e) the potential difference across R2f) the potential difference across Lg) the rate of current change across R1... Get solution
53. In the circuit in the figure, a battery supplies Vemf = 18.0 V and R1 = 6.00 Ω, R2 = 6.00 Ω, and L = 5.00 H. Calculate each of the following a long time after the switch is closed:a) the current flowing out of the batteryb) the current through R1c) the current through R2d) the potential difference across R1e) the potential difference across R2f) the potential difference across Lg) the rate of current change across R1... Get solution
54. A circuit contains a battery, three resistors, and an inductor, as shown in the figure. What will be the current through each resistor (a) immediately after the switch is closed and (b) a long time after the witch is closed? (c) Suppose the switch is reopened a long time after it has been closed. What is the current in each resistor? After a long time?... Get solution
55. Having just learned that there is energy associated with magnetic fields, an inventor sets out to tap the energy associated with the Earth’s magnetic field. What volume of space near Earth’s surface contains 1.00 J of energy, assuming the strength of the magnetic field to be 5.00 · 10–5 T? Get solution
56. A clinical MRI (magnetic resonance imaging) superconducting magnet can be approximated as a solenoid with a diameter of 1.00 m, a length of 1.50 m, and a uniform magnetic field of 3.00 T. Determine (a) the energy density of the magnetic field and (b) the total energy in the solenoid.... Get solution
57. A magnetar (magnetic neutron star) has a magnetic field near its surface of magnitude 4.00 · 1010 T.a) Calculate the energy density of this magnetic field.b) The Special Theory of Relativity associates energy with any mass m at rest according to E0 = mc2 (more on this in Chapter 35). Find the rest mass density associated with the energy density of part (a). Get solution
58. An emf of 20.0 V is applied to a coil with an inductance of 40.0 mH and a resistance of 0.500 Ω.a) Determine the energy stored in the magnetic field when the current reaches ¼ of its maximum value.b) How long does it take for the current to reach this value? Get solution
59. A student wearing a 15.0-g gold band with radius 0.750 cm (and with a resistance of 61.9 µΩ and a specific heat capacity of c = 129 J/kg °C) on her finger moves her finger from a region having a magnetic field of 0.0800 T, pointing along her finger, to a region with zero magnetic field in 40.0 ms. As a result of this action, thermal energy is added to the band due to the induced current, which raises the temperature of the band. Calculate the temperature rise in the band, assuming that all the energy produced is used in raising the temperature. Get solution
60. A coil with N turns and area A, carrying a constant current, i, flips in an external magnetic field, ... so that its dipole moment switches from induction produces a potential difference that tends to reduce the current in the coil. Calculate the work done by the coil’s power supply to maintain the constant current. Get solution
61. An electromagnetic wave propagating in vacuum has electric and magnetic fields given by ... and ... where ... is given by ... and the wave vector ... is perpendicular to both ... and .... The magnitude of ... and the angular frequency ω satisfy the dispersion relation, ... where µ0 and ε0 are the permeability and permittivity of free space, respectively. Such a wave transports energy in both its electric and magnetic fields. Calculate the ratio of the energy densities of the magnetic and electric fields, uB/uE, in this wave. Simplify your final answer as much as possible. Get solution
62. A wire of length ... = 10.0 cm is moving with constant velocity in the xy-plane; the wire is parallel to the y-axis and moving along the x-axis. If a magnetic field of magnitude 1.00 T is pointing along the positive z-axis, what must the velocity of the wire be in order for a potential difference of 2.00 V to be induced across it? Get solution
63. The magnetic field inside the solenoid in the figure changes at the rate of 1.50 T/s. A conducting coil with 2000 turns surrounds the solenoid, as shown. The radius of the solenoid is 4.00 cm, and the radius of the coil is 7.00 cm. What is the potential difference induced in the coil?... Get solution
64. An ideal battery (with no internal resistance) supplies Vemf and is connected to a superconducting (no resistance!) coil of inductance L at time t = 0. Find the current in the coil as a function of time, i(t). Assume that all connections also have zero resistance. Get solution
65. A 100-turn solenoid of length 8.00 cm and radius 6.00 mm carries a current of 0.400 A from right to left. The current is then reversed so that it flows from left to right. By how much does the energy stored in the magnetic field inside the solenoid change? Get solution
66. The electric field near the Earth’s surface has a magnitude of 150. N/C, and the magnitude of the Earth’s magnetic field near the surface is typically 50.0 µT. Calculate and compare the energy densities associated with these two fields. Assume that the electric and magnetic properties of air are essentially those of a vacuum. Get solution
67. What is the inductance in a series RL circuit in which R = 3.00 kΩ if the current increases to ½ of its final value in 20.0 µs? Get solution
68. A 100.-V battery is connected in series with a 500.-Ω resistor. According to Faraday’s Law of Induction, current can never change instantaneously, so there is always some “stray” inductance. Suppose the stray inductance is 0.200 µH. How long will it take the current to build up to within 0.500% of its final value of 0.200 A after the resistor is connected to the battery? Get solution
69. A single loop of wire with an area of 5.00 m2 is located in the plane of the page, as shown in the figure. A time-varying magnetic field in the region of the loop is directed into the page, and its magnitude is given by B = 3.00 T + (2.00 T/s)t. At t = 2.00 s, what are the induced potential difference in the loop and the direction of the induced current?... Get solution
70. A 9.00-V battery is connected through a switch to two identical resistors and an ideal inductor, as shown in the figure. Each of the resistors has a resistance of 100. Ω, and the inductor has an inductance of 3.00 H. The switch is initially open.a) Immediately after the switch is closed, what is the current in resistor R1 and in resistor R2?b) At 50.0 ms after the switch is closed, what is the current in resistor R1 and in resistor R2?c) At 500. ms after the switch is closed, what is the current in resistor R1 and in resistor R2?d) After a long time (> 10.0 s), the switch is opened again. Immediately after the switch is opened, what is the current in resistor R1 and in resistor R2?e) At 50.0 ms after the switch is opened, what is the current in resistor R1 and in resistor R2?f) At 500. ms after the switch is opened, what is the current in resistor R1 and in resistor R2?... Get solution
71. A long solenoid with length 3.00 m and n = 290. turns/m carries a current of 3.00 A. It stores 2.80 J of energy. What is the cross-sectional area of the solenoid? Get solution
72. A rectangular conducting loop with dimensions a and b and resistance R is placed in the xy-plane. A magnetic field of magnitude B passes through the loop. The magnetic field is in the positive z-direction and varies in time according to B = B0(1 + c1t3), where c1 is a constant with units of 1/s3. What is the direction of the current induced in the loop, and what is its value at t = 1 s (in terms of a, b, R, B0, and c1)? Get solution
73. A circuit contains a 12.0-V battery, a switch, and a light bulb connected in series. When the light bulb has a current of 0.100 A flowing in it, it just starts to glow. This bulb draws 2.00 W when the switch has been closed for a long time. The switch is opened, and an inductor is added to the circuit, in series with the bulb. If the light bulb begins to glow 3.50 ms after the switch is closed again, what is the magnitude of the inductance? Ignore any time needed to heat the filament, and assume that you are able to observe a glow as soon as the current in the filament reaches the 0.100-A threshold. Get solution
74. A circular loop of area A is placed perpendicular to a time-varying magnetic field of magnitude B(t) = B0 + at + bt2, where B0, a, and b are constants.a) What is the magnetic flux through the loop at t = 0?b) Derive an equation for the induced potential difference in the loop as a function of time.c) What are the magnitude and the direction of the induced current if the resistance of the loop is R? Get solution
75. A conducting rod of length 50.0 cm slides over two parallel metal bars placed in a magnetic field with a magnitude of 1.00 kG, as shown in the figure. The ends of the rods are connected by two resistors, R1 = 100. Ω and R2 = 200. Ω. The conducting rod moves with a constant speed of 8.00 m/s.a) What are the currents flowing through the two resistors?b) What power is delivered to the resistors?c) What force is needed to keep the rod moving with constant velocity?... Get solution
76. A rectangular wire loop (dimensions of h = 15.0 cm and w = 8.00 cm) with resistance R = 5.00 Ω is mounted on a door, as shown in the figure. The Earth’s magnetic field, BE = 2.60 · 10–5 T, is uniform and perpendicular to the surface of the closed door (the surface is in the xz-plane). At time t = 0, the door is opened (right edge moves toward the y-axis) at a constant rate, with an opening angle of θ(t) = ωt, where ω = 3.50 rad/s. Calculate the direction and the magnitude of the current induced in the loop, i(t = 0.200 s)....... Get solution
77. A steel cylinder with radius 2.50 cm and length 10.0 cm rolls without slipping down a ramp that is inclined at 15.0° above the horizontal and has a length (along the ramp) of 3.00 m. What is the induced potential difference between the ends of the cylinder as the cylinder leaves the bottom of the ramp, if the downward slope of the ramp points in the direction of the Earth’s magnetic field at that location? (Use 0.426 G for the local strength of the Earth’s magnetic field.) Get solution
78. The figure shows a circuit in which a battery is connected to a resistor and an inductor in series.a) What is the current in the circuit at any time t after the switch is closed?b) Calculate the total energy provided by the battery from t = 0 to t = L/R.c) Calculate the total energy dissipated in the resistor over the same time period.d) Is energy conserved in this circuit?... Get solution
79. As shown in the figure, a rectangular (60.0 cm long by 15.0 cm wide) circuit loop with resistance 35.0 Ω is held parallel to the xy-plane with one half inside a uniform magnetic field. A magnetic field given by ... = 2.00ẑ T is directed along the positive z-axis to the right of the dashed line; there is no external magnetic field to the left of the dashed line.a) Calculate the magnitude of the force required to move the loop to the left at a constant speed of 10.0 cm/s while the right end of the loop is still in the magnetic field.b) What power is expended to pull the loop out of the magnetic field at this speed?c) What is the power dissipated by the resistor?... Get solution
81. What is the inductance in an RL circuit with R = 17.88 Ω if the time required for the current to reach 75% of its maximum value is 3.450 ms? Get solution
82. For an RL circuit with R = 21.84 Ω and L = 55.93 mH, how long does it take the current to reach 75% of its maximum value? Get solution
83. A wedding ring (of diameter 1.95 cm) is tossed into the air and given a spin, resulting in an angular velocity of 13.3 rev/s. The rotation axis is a diameter of the ring. If the magnitude of the Earth’s magnetic field at the ring’s location is 4.77 · 10–5 T, what is the maximum induced potential difference in the ring? Get solution
84. A wedding ring is tossed into the air and given a spin, resulting in an angular velocity of 13.5 rev/s. The rotation axis is a diameter of the ring. .The magnitude of the Earth’s magnetic field is 4.97 · 10–5 T at the ring’s location. If the maximum induced voltage in the ring is 1.446 · 10–6 V, what is the diameter of the ring? Get solution
85. A wedding ring of diameter 1.63 cm is tossed into the air and given a spin, resulting in an angular velocity of 13.7 rev/s. The rotation axis is a diameter of the ring. If the maximum induced voltage in the ring is 6.556 · 10–7 V, what is the magnitude of the Earth’s magnetic field at this location? Get solution
