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If a capacitor is being charged or in the process of discharge, there is current flowing in/out of the conductive plate, besides the magnetic field produced by the displacement currents($B_{dc}$) in the separation gap, wouldn't there be a transient magnetic field from the plates as well?

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There should be some small transient magnetic field due to radial currents in the plates, but, since the currents in the two plates flow in opposite directions and the plates are typically close to each other, most of this field is likely to be cancelled.

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  • $\begingroup$ Makes sense, however, I'm curious about this: Why is the current flow radial? I imagined the current flowing outwards in equipotential. $\endgroup$
    – e.d.m
    Jul 30, 2018 at 20:42
  • $\begingroup$ @co99 Not sure what you mean by "equipotential" in this context. When I say radial, I mean that the currents flow in all directions from the center of a plate, where the wire makes a contact with the plate, along radii, to the edge of the plate. So, essentially, they flow outwards (or inwards, if negative). Radial direction=direction along a radius. $\endgroup$
    – V.F.
    Jul 30, 2018 at 20:54
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While charging a capacitor there will be a magnetic field present due to the change in the electric field. And of course contains energy as pointed out. However: As the capacitor charges, the magnetic field does not remain static. This results in electromagnetic waves which radiate energy away.

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