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So, I know that changing magnetic field produces a non electrostatic electric field which goes around in circles. My question is how do we know they are circular in nature? If I'll put a square wire in changing magnetic field then the current must go in a square and so should the electric field. Isn't it right?Why is induced electric field circular and also who decides the center of these circular induced electric field? Can't the center of these circles be anywhere?

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  • $\begingroup$ > "which goes around in circles" -- that is true only in a very special situation, where the magnetic field has cylindrical symmetry. In most cases, the magnetic and thus also the electric field is more complicated. $\endgroup$ – Ján Lalinský Oct 21 '18 at 23:22
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The electric field would shoot out radially from the wire. The magnetic field would loop around in circles. The E and B field must always be orthogonal; the B field runs tangent to the circumference of the wire while the E field is normal to it's surface. How we know they are orthogonal is how we know everything else; we observe it, over, and over, and over again. Mathematically we then represent it with the cross product.

Now as for the whole square thing, how the [individual] E and B vectors generated from a single point on the wire add onto one another to create the TOTAL E and B fields for a given geometry... that can get messy. Symmetry helps. In the case of square I don't recall off the top of my head though.

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  • $\begingroup$ I think I didn't explained my question correctly. My question is, why are the induced electric field circular in nature?(also there is no wire here, it is just a plane through which magnetic field is increasing) $\endgroup$ – user157725 Jun 1 '17 at 20:30
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In absence of other elements, the shape adopted will be circular due to the simmetry. Else there would be "priviledged" or "favoured" directions, but that does not make sense because rotating the system should not make any change, as the source elements are indistinguishable from the previous situation. Once you introduce a "distubing element" you are changing the boundary conditions and the fields adapt to it.

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  • $\begingroup$ But how do we define the center of these circles? Since there exists translational symmetry, any other point could also have been the center of these induced electric field. $\endgroup$ – user157725 Jun 1 '17 at 21:02
  • $\begingroup$ If there is not a definite center (like, for example, if there's a point from which the field decays) then there can't be circles, because each part of a vortex cancels with the opposite part of its neighbour. There would only be a circle around the frontier (and if it's infinite, then there is not any). Maybe I didn't understand your question well. Anyway, any answer you can be seeking for is surely codified in the Maxwell equations. $\endgroup$ – FGSUZ Jun 1 '17 at 21:26

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