Magnetic field induced by a charging infinite plane

[ItachiUchiha]

It's a routine to calculate the magnetic field between circular capacitor plates by the Ampere-Maxwell law, and it can be shown that the magnetic field increases linearly with the distance from the center of the capacitor plates, with direction parallel to the plates.

But what if the radius of the capacitor plates tends to infinite? Or, put it the other way, what is the magnetic field between two opposite charged infinite planes, assuming the surface charge density increases at a constant rate σ per second?

Or even simpler, as the title asks, what is the magnetic field induced by a charging infinite plane?

 

[madhatter106]

That's a very good question, an infinite plane would have an infinite answer by definition. must keep to the limit of C per relativity. Not sure on what the rules are on speculation of faster than C, however superluminal ES waves are due to the magnetic field being parallel to the electric field. This is a phenomenon in lightning, pulsars and some high energy plasma research.

If you're asking what direction the field polarity is in then it's circular per the Ampere-Maxwell law as the conjugate E&M pairing dictates. There is also I believe a hyperbolic curve of intensity from the center to the edge, but with an infinite plane it would approach an asymptote I think.