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Jay21

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I have a question regarding Maxwell's Equations and Faraday's unipolar induction equation.

If we study the case of a cylindrical magnet with a radius of r which is rotating about its axis

with angular velocity w. The electrons within the magnet collide with the moving atoms, causing

a net drift velocity, v = w x r. The electrons experience a force:

-e*(v x B) towards the center

This results in the negative charge being centralized in the magnet and a positive

charge on the outer surface, thus creating an equilibrium electrostatics field with

Lorentz force:

F = -eE - e*(v x B) = 0

This leads to the unipolar induction equation of

E = - v x B

My question is that while studying plasma physics I came across a very similar equation such that

H = v x D

How would one derive this analogous equation of the unipolar induction equation?

I read somewhere that you could derive this equation by using a thin, charged rotating ring,

but I am unsure as to how to accomplish this.

Thanks so much.

Jay

Citations I have investigated trying to derive this analgous equation:

Unipolar Induction via a Rotating, Conducting, Magnetized Cylinder by Kirk T. McDonald

for in a comoving inertia frame

H* = H - ((v/c) x D)

Basic Plasma Physics Principles by Gordon Emslie for

E' = gamma*(E + (v/c) x B)

B' = gamma*(B - (v/c) x E)

The Unipolar Induction by P. Hrasko for

B = (u_0*gamma)*H + (1/c^2)(v x E)