A long straight wire carrying current I is moving with speed v toward a small ci

Question

A long straight wire carrying current I is moving with speed v toward a small circular coil of radius r containing N turns, which is attached to a voltmeter as shown. The long wire is in the plane of the coil. (Only a small portion of the wire is shown in the diagram.) The radius of the coil is 0.02 m, and the coil has 11 turns. At a particular instant I = 3 amperes, v = 2.9 meters per second, and the distance from the wire to the center of the coil x = 0.13 m. What is the magnitude of the rate of change of the magnetic field inside the coil? You will need to calculate this algebraically before you can get a number. Write an expression for the magnetic field due to the wire at the location of the coil. Use the approximate formula, since the wire is very long. Remember the chain rule, and remember that v = dx/dt. dB/dt = T/s What is the magnitude of the voltmeter reading? Remember that this includes all 11 turns of the coil. volts What is the direction of dB/dt? Select What is the direction of the curly electric field in the coil? Select

Explanation / Answer

According to the given problem,

A.) Since B is inversely proportional to x,

we can say that dB/B = -dx/x, or

dB/dt = -B(dx/dt)/x = -Bv/x.

B = 2nu0I/4r = 3.3 * 10-4 T

dB/dt = -3.3 * 10-4*2.9/0.13 = -7.3615*10-3 T/s

B.) Area A = 0.022 = 1.2566 10-3 m2

V = N*d[B*A]/dt

V = NA*dB/dt

V = 11*1.2566 10-3*7.3615*10-3V

V = 1.0175*10-4Volts

C.) Out of the coil and towards +x axies

D.) It is out of the page and towards +z axies

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