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

["Michael N. Monce" <mnmon@CONNCOLL.EDU>]

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