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Electric to be

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∮E(t0)⋅dℓ= −dΦ(t)/dt|t=t0Say for a long time, in some circular region there has been no B or E fields present. Then, there is a sudden constant increase of B field introduced in the middle. I know that information cannot propagate faster than the speed of light, but doesn't Maxwell's equation predict that at that instant, there should be some nonzero integral of the E field at some radius R away from the newly introduced B field? Is Maxwell's equation wrong in this area? This equation written explicitly doesn't somehow tell me that, "Oh there will be a field there, but only after a few instants once there has been sufficient time for that information to spread" haha.

Or does the integral form somehow not hold? (I thought integral and differential form are equivalent, by Stoke's/Divergence Theorem)

Thanks for any help in clearing up this doubt.