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Refer to the image

In question, it is explicitly mentioned that the coil is placed in the uniform magnetic. When the coil is not in the magnetic field, the current flowing through the coil is zero; hence the change of magnetic flux is also zero. But when the coil is placed in the Magnetic field the magnetic flux through the coil changes suddenly; hence due to the change in flux there should be an EMF and a current. Let's say at t=0, we place the coil so according to me there should be current at that instant but afterwards the current must remain constant because the flux is no longer changing through the coil. Therefore option d should be the answer but the answer is c. Can anyone please explain this inconsistency?

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  • $\begingroup$ Sometimes, with multiple-choice, the trick is figuring out which is the best answer. Sometimes you won't see any answer that is exactly right, and the puzzle is, to figure out which one they wanted you to choose. In this case, "when the...magnetic flux...changes suddenly," there will be some kind of transient behavior. But none of the four choices shows anything that looks like a transient. So, you might guess instead that they are asking for the steady state behavior. After the coil stops moving, after everything settles down, then which of those four pictures would you choose? $\endgroup$
    – Solomon Slow
    Commented Oct 20, 2023 at 17:34

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The wording of the question, "... is placed in a uniform magnetic field ..." has (understandably) misled you. The question setter wants you to assume, when picking an answer, that the coil is ALREADY in the field and undergoing shm as described. How do I know this? Experience! [And that none of the offered answers would fit if placing the coil in the field were part of the process to be shown in the graph, as there would be an initial spike.]

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I think that the question is badly posed. If the coil was put in the uniform magnetic field, a current would arise to compensate for the flux variation. This current would then decay to $0$ due to the wire resistance. From now on, if the coil is moved along the field direction, no flux variation occurs and therefore no current is flowing. It is clear that none of the answers is describing this situation. The only way to get $c$ as the correct answer is if the coil has always been immersed inside the uniform magnetic field.

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  • $\begingroup$ "if the coil is moved along the field direction, no flux variation occurs and therefore no current is flowing" You are right that now $d\Phi/dt=0$, but this is not a good enough explanation for zero induced current, recall the Faraday homopolar dynamo. The difference between the two cases is that here the force and thus the free charges (electrons) would have to move parallel with the magnetic field, hence $\mathbf v\times \mathbf B = 0$, and no induced current along the wire* that is perpendicular to that motion. $\endgroup$
    – hyportnex
    Commented Oct 20, 2023 at 18:53

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