# Vector potential

1. Aug 16, 2007

### captain

i am having trouble visualiszing what vector potential A means physically. I understand that if you take the curl of it it give you the magnetic field B. I was wondering if anybody could also direct me to a website or show me a proof of how the electric field E is equal to the partial derivative of A with respect to time minus the grad of the scalar potential. I have no clue where to find that proof and neither do i possess a text book that has the proof in it.

2. Aug 16, 2007

### Pythagorean

I still don't understand the physical significance of A. My teacher told me there wasn't really one... it was just a mathematical relationship. Anyway, it seems to be in the same direction the E field that gets induced by the B field (which may or may not be induced by an original field, E1)

how E = dA/dt:

use Maxwell's Equations, maybe the divergence theorem or one of those other integral forms.... I'm having deja vu:

http://en.wikipedia.org/wiki/Maxwell's_equations

3. Aug 16, 2007

### marlon

Your teacher is right on this one. The A-potential is introduced in the EM formalism to write the theory in a symmetrical way. It makes the step towards field theory more logic in the sense that the A field plays the role of the EM gauge field. Also, this potential is used to impose gauge-conditions to set the remaining degree of freedom that arises due to the definition of the A-field.

More here : http://en.wikipedia.org/wiki/Magnetic_potential

marlon

edit : you should also wonder about the question why they call the A field a POTENTIAL ! (hint : look at the definition of the scalar potential)

Last edited: Aug 16, 2007
4. Aug 16, 2007

### captain

Last edited by a moderator: May 3, 2017