# How to picture the magnetic vector potental A

whats a good way to picture the vector potental A in terms of B & like what exactly is A & how does it even exist outside a torus where B & etc =0

for example its easy to see the electric potential uses the electric field E like E*ds & its quite obvious,
wheras how does A not even contain the B field

also why is A sometimes said to not even exist or is just a paper shortcut when it actualy seems to work or exist in some way. thanks

Since the curl of the vector potential A is equal to the magnetic field B, a good way to think of it is that A circulates around any point where B is nonzero--its net circulation around a point gives the B field at that point, according to the right-hand rule. It is important to remember though that you can always write down different A's to produce the same B field--this is called choosing a gauge. For example, a uniform B field in the z direction could be represented by any of the following:
A = -By i
A = Bx j
A = -By/2 i + Bx/2 j
where i is the unit vector in the x direction, and j is the unit vector in the y direction, and B is the magnitude of B.
If you plot these, you will see that they all look quite different, but they all circulate around in a similar fashion.

In classical E&M, the B field is the measurable quantity, so A is said to just be a mathematical convenience. However, in quantum physics, particles can be affected by magnetism even if they never pass through a region of nonzero B--instead they directly interact with A. A good example is the Aharanov-Bohm effect: http://en.wikipedia.org/wiki/Aharanov-Bohm_effect

WannabeNewton