Additional Problems

| 62 | In each of two coils the rate of change of the magnetic flux in a single loop is the same. The emf induced in coil 1, which has 184 loops, is 2.82 V. The emf induced in coil 2 is 4.23 V. How many loops does coil 2 have?

| 63 | ssm www The drawing shows a plot of the output emf of a generator as a function of time t. The coil of this device has a cross-sectional area per turn of 0.020 m2 and contains 150 turns. Find (a) the frequency f of the generator in hertz, (b) the angular speed in rad/s, and (c) the magnitude of the magnetic field.

| 64 | Magnetic resonance imaging (MRI) is a medical technique for producing pictures of the interior of the body. The patient is placed within a strong magnetic field. One safety concern is what would happen to the positively and negatively charged particles in the body fluids if an equipment failure caused the magnetic field to be shut off suddenly. An induced emf could cause these particles to flow, producing an electric current within the body. Suppose the largest surface of the body through which flux passes has an area of 0.032 m2 and a normal that is parallel to a magnetic field of 1.5 T. Determine the smallest time period during which the field can be allowed to vanish if the magnitude of the average induced emf is to be kept less than 0.010 V.

| 65 | ssm In Figure 22-1, suppose the north and south poles of the magnet were interchanged. Determine the direction of the current through the ammeter in parts b and c of the picture (left to right or right to left). Give your rationale.

| 66 | In some places, insect “zappers,” with their blue lights, are a familiar sight on a summer’s night. These devices use a high voltage to electrocute insects. One such device uses an ac voltage of 4320 V, which is obtained from a standard 120.0-V outlet by means of a transformer. If the primary coil has 21 turns, how many turns are in the secondary coil?

| 67 | ssm The coil within an ac generator has an area per turn of 1.2 × 10−2 m2 and consists of 500 turns. The coil is situated in a 0.13-T magnetic field and is rotating at an angular speed of 34 rad/s. What is the emf induced in the coil at the instant when the normal to the loop makes an angle of 27° with respect to the direction of the magnetic field?

* | 68 | A magnetic field has a magnitude of 12 T. What is the magnitude of an electric field that stores the same energy per unit volume as this magnetic field?

* | 69 | Parts a and b of the drawing show the same uniform and constant (in time) magnetic field directed perpendicularly into the paper over a rectangular region. Outside this region, there is no field. Also shown is a rectangular coil (one turn), which lies in the plane of the paper. In part a the long side of the coil (length = L) is just at the edge of the field region, while in part b the short side (width = W) is just at the edge. It is known that L/W = 3.0. In both parts of the drawing the coil is pushed into the field with the same velocity until it is completely within the field region. The magnitude of the average emf induced in the coil in part a is 0.15 V. What is its magnitude in part b?

* | 70 | Indicate the direction of the electric field between the plates of the parallel plate capacitor shown in the drawing if the magnetic field is decreasing in time. Give your reasoning.

Problem 70

* | 71 | ssm A magnetic field is passing through a loop of wire whose area is 0.018 m2. The direction of the magnetic field is parallel to the normal to the loop, and the magnitude of the field is increasing at the rate of 0.20 T/s. (a) Determine the magnitude of the emf induced in the loop. (b) Suppose the area of the loop can be enlarged or shrunk. If the magnetic field is increasing as in part (a), at what rate (in m2/s) should the area be changed at the instant when B = 1.8 T if the induced emf is to be zero? Explain whether the area is to be enlarged or shrunk.

* | 72 | The purpose of this problem is to show that the work W needed to establish a final current If in an inductor is (Equation 22.10). In Section 22.8 we saw that the amount of work needed to change the current through an inductor by an amount is , where L is the inductance. The drawing shows a graph of LI versus I. Notice that is the area of the shaded vertical rectangle whose height is LI and whose width is . Use this fact to show that the total work W needed to establish a current If is .

** | 73 | Two 0.68-m-long conducting rods are rotating at the same speed in opposite directions, and both are perpendicular to a 4.7-T magnetic field. As the drawing shows, the ends of these rods come to within 1.0 mm of each other as they rotate. Moreover, the fixed ends about which the rods are rotating are connected by a wire, so these ends are at the same electric potential. If a potential difference of 4.5 × 103 V is required to cause a 1.0-mm spark in air, what is the angular speed (in rad/s) of the rods when a spark jumps across the gap?

** | 74 | The armature of an electric drill motor has a resistance of . When connected to a 120.0-V outlet, the motor rotates at its normal speed and develops a back emf of 108 V. (a) What is the current through the motor? (b) If the armature freezes up due to a lack of lubrication in the bearings and can no longer rotate, what is the current in the stationary armature? (c) What is the current when the motor runs at only half speed?

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