# What does B = del x A mean?

1. Mar 31, 2009

### lalligagger

1. The problem statement, all variables and given/known data

Not going to write out the whole problem (yet). It's a "find the error in the incorrect proof" type of question in a section on curl and divergence.

2. Relevant equations

B = $$\nabla$$x A is given as an equation of "electromagnetic theory" and used in the proof. It's stated that the error is not in this equation. The other equation used in the proof is Gauss's Law for magnetic fields, but I get that one.

3. The attempt at a solution

Haven't really tried; I'd like to know the physical interpretation of the above equation before I start staring at integrals. I just got through electricity and magnetism in my general physics course, but this doesn't look familiar. I'm assuming that A is some type of force field, but what field would satisfy the equation?

2. Mar 31, 2009

### LowlyPion

Well μH = ∇ X A

Magnetic Force

3. Mar 31, 2009

### lalligagger

Thanks Pion, but can you elaborate? What is μH and how does it relate to B?
BTW, this is for a course that basically covers vector calculus that our math department doesn't in early calc classes. The question is really just about applying Stoke's theorem, which I understand pretty well. It's just the one equation that I don't get is keeping me from even starting the problem.
I can try and scan the problem if more context is needed, but it's nothing I want to write out here.

4. Mar 31, 2009

### lalligagger

Ok, A is the vector potential of B. Does A have any physical meaning or is it just an arbitrary vector that must exist because $$\nabla$$$$\bullet$$B=0?

5. Mar 31, 2009