If you try to solve Maxwell's equations with a current distribution
that just terminates in the middle of nowhere, then Maxwell's
equations will actually pile up charges on the ends of that
distribution for you.
This is because Maxwell's equations have "charge continuity" built
into them. Remember this one?
curl H = J + epsilon * dE/dt
If you take the divergence of this equation, you get
div curl H = 0 = div J + d[ div( epsilon * E ) ] / dt
But div( epsilon * E ) = Q (this is another of Maxwell's equations, known
as Gauss' law), and so we get
div J + dQ / dt = 0
There's a big divergence to J where the current distribution abruptly
terminates, and so there's a dQ/dt there to balance this.
Fortunately, even time-varying charges don't contribute to the magnetic
vector potential A. It's computed by integrating over all the currents
A = Integral[ (Green's function) * J ]
The vector potential is used in the energy definition of inductance:
Wm = (1/2)*Integral[ A * J ] = 1/2 * L * I^2.
So, the piling-up charges DO NOT affect the inductance calculation in
any way. Therefore, they may safely be neglected, and indeed they are.
Sorry to drag anybody through this muck, who, really, didn't give
a damn.
-- J. Eric Bracken, Ph.D. Tel: 1.412.261.3200 x135 Group Leader, Signal Integrity R&D Fax: 1.412.471.9427 Ansoft Corp., Four Station Square, Suite 660 [email protected] Pittsburgh, PA USA 15219-1119 http://www.ansoft.com