Re: [Phys-l] electric potential

[John Denker <jsd@av8n.com>]

On 08/30/2010 05:57 AM, carmelo@pacific.net.sg wrote:

> One student just explains to me that "there is no such entity as  
> electric potential, there is only potential difference". He attributes  
> this explanation to his physics teacher who is trained in engineering.  
> This explanation helps him in problem solving. Do you agree with this  
> explanation or pedagogical approach?

Actually, focusing attention on "The" electric potential is
a bad idea for two reasons:

*) The first reason is gauge invariance, as alluded to above.
In situations where there is an electric potential, statements
about _potential difference_ are gauge-invariant, whereas
statements about the potential itself are not gauge-invariant.

Gauge invariance is a profoundly important symmetry of the laws
of electromagnetism.  I get 32 hits from
  http://ipv6.google.com/search?q=%22gauge+invariance%22+site%3Anobelprize.org


*) It is a mistake to overemphasize electric potential *or* 
potential differences, because in many situations the electric
field is not the gradient of any potential.

The electric field is what matters.  Assuming that the electric
field is the gradient of The potential is a bad idea.  This is
a very common mistake.

Note that Kirchhoff's Voltage Law is based on this dubious assumption.

============

As to the "explanation" and the "pedagogical approach" I would 
say that the guy didn't even attempt an explanation.  An assertion
is not an explanation.  Still, though, the assertion was correct.