Re: Faraday induction

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding John Denker's definition of 05/31/01:

> At 09:51 AM 5/31/01 -0400, Eugene Mosca wrote:
> > Is there a conventional definition of voltage?  If so, what is it?
>
> How about energy per unit charge?

I don't know about whether it is "conventional" or not (as I have not
heard of any convention endorsing it), but it seems to me that the phrase
"energy per unit charge" is open to various kinds of misinterpretations
as to the meaning of the term 'voltage' (mostly because there are so many
different kinds of energy extant, and also because of the lack of a
uniquely definable potential energy in the case of time-variable magnetic
fields).

I would prefer to modify the above definition of 'voltage' so that it is
considered to be the "electric *work* per unit charge" done on a 'test'
charge by the electric field when it is moved virtually and
quasi-statically from one point in space to another point.  *If* the
corresponding electric field in the region of space containing those two
points is curl-free, a potential voltage exists and an electric potential
value can be assigned to each point in space in such a region up to an
arbitrary 'zero level' (in any gauge in which the magnetic A-potential is
static).  In such a case the voltage between any two points in such a
region of space is just the difference in the values of the electric
potential at those two points.  If a time dependent magnetic field is
present then there is no assignment of electric potential values in space
such that the gradient of that potential completely determines that
electric field, and whose differences determine the voltages between
pairs of points.  The voltage between a pair of points is then only
determined by a further specification of the actual path traveled in
space by the 'test' charge between those two points for which the voltage
is to be found.  (In this later case there is also no gauge in which the
magnetic A-potential is static.)

David Bowman
David_Bowman@georgetowncollege.edu