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I've been told that a cylindrical time-varying magnetic field induces a non-conservative electric field shaped like circles centred at the axis of the cylindrical magnetic field. I suppose it's an experimental observation.

As we increase the radius of this cylinder, I can expect that the centre of the induced electric field remains at the centre of the cylinder. However, what bothers me is that when the cylinder's radius tends to infinity, there really is no defined position for the 'centre'.

Question: So how can we judge where the centre of the induced electric field will lie, if the varying magnetic field that induces it fills an infinite space? Additionally, how can we judge where the centre will lie if the magnetic field takes an arbitrary shape? (I know the position matters as it will influence the motion of charges in the space)

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  • $\begingroup$ If a mathematical answer is acceptable, you can find one here: Electric Field in a uniform time-varying Magnetic field. Are you looking for a non-mathematical answer? $\endgroup$
    – Chiral Anomaly
    Commented May 2, 2020 at 19:17
  • $\begingroup$ @ChiralAnomaly Yeah, I don't know much of the math involved in vector fields. I'm just looking for a straightforward answer. $\endgroup$
    – Nikhil Anand
    Commented May 3, 2020 at 1:28

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