A bar magnet induces a current in an N -turn coil as the magnet moves closer to

Question

A bar magnet induces a current in an N-turn coil as the magnet moves closer to it as shown in (Figure 1) . The coil's radius is R m, and the average induced emf across the bulb during the time interval is V.

Part A

Find the rate of change of magnetic field.

Express your answer in terms of the variables , N, R, and appropriate constants.

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Part B

Determine the induced current. Assume that R0 is the resistance of the coil.

Express your answer in terms of some or all of the variables , N, R, R0.

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Part C

Is the direction of the induced current from lead a to b, or from b to a?

Is the direction of the induced current from lead a to b, or from b to a?

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Explanation / Answer

Flux through loop:

Q = N*B*(pi*R^2)

So, rate of change of flux, dQ/dt = N*(pi*R^2)*dB/dt

Now, dQ/dt = induced EMF = epsilon

So, epsilon = N*(pi*R^2)*dB/dt

So, dB/dt = epsilon/(pi*R^2*N). <--------- answer

B)

Induced current = induced EMF / resistance

= epsilon/R0

C)

Magnetic field lines are increasing in the upward direction as the magnet comes down. So, induced magnetic field must be directed in opposite direction(as per Lenz Law). So, induced magnetic field will be directed in downward direction and for this to happen current needs to flow in counterclockwise direction(looking from above). So, current will flow from( b to a) in the wire.

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