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I've always had this question and didn't know how to answer it - Why do eddy currents have the shape they do? Why are they circular eddies?

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$Are\ you\ sure\ they\ are\ always\ circular?\ Then\ I\ think\ you\ are\ wrong.$
Eddy current
Example of non circular Eddy current


Definition of Eddy Current: They are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field.
The Eddy currents flow in loop but the shape of loop is depends on shape of the conductor.

Why are they in closed loop? Actually they are opposing the magnetic field. The loop shape can be understood by Lenz's Law and Right Hand Thumb Rule.

For more details you can see this link Eddy Current

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