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Suppose the complete space is filled with magnetic field of $\vec{B} = B_0 t(-\hat{i})$, where $t$ is time, there are two cases

  1. There is a circular conductor ring with its plane perpendicular to direction of magnetic field and axis along the magnetic field.

  2. There is no conductor, nothing except time varying magnetic field.

What will be the shape of induced electric field?
Will it be circular in both cases?
If so, will both circular field have common centre?
If both have common centre, how could the case 2 have specified centre, when the centre could have been anywhere in space?

And finally, how will the overall picture of electric field line look like? If possible explain with diagram.

It would be nice if you do not use curl operator to explain, as I am not friendly with it.

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