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Re: induced emf again



On Wed, 1 May 2002, Ludwik Kowalski wrote:

1) What still bothers me is this. The emf=B*v*L can
also be derived from Faraday's law of induction.

d(flux)/dt = B*d(area)/dt=B*L*dx/dt = B*L*v

This derivation does not imply any gradients of charge
density;

True enough.

it contradicts the existence of such gradients.

Why do you say that? You don't need any charge density gradients
to have an emf, but you do if you want the resulting current to be
steady and divergenceless. In other words, the emf (equivalent to
the vxB force) initially gets the charge moving, but the specific
*pattern* of current is unsustainable because it has a nonzero
divergence and, therefore, produces increasing polarization
charges. Very quickly and in a self-consistent manner, those
polarization charges adjust themselves to produce a dynamic
equilibrium in which the current is steady and divergenceless (as
they do in every DC circuit.)

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm