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Re: non-potential voltages vs. Kirchhoff's laws



On Wed, 14 Apr 1999, John Denker wrote:


3) If you can't tell me the voltage as a function of position, it is not
possible to take the gradient thereof. The question of whether this
non-existent gradient should be called an electric field is moot.

jsd


I think it is still an E-field. We have curlE = -dB/dt, and
curlB = A, so curl E = -d/dt(curl A). Rearrange:

curl (E + dA/dt) = 0

Since the curl of a gradient is zero, we can define the scaler potential
V such that

E + dA/dt = -grad V

or

E = -grad V - dA/dt , otherwise known as the 4-vector
potential.

This really shows the two sources of the E-field: charges (grad
V), *and* the changing mag. field (dA/dt).


Mike Monce
Connecticut College