Register to reply

How to picture the magnetic vector potental A

by si22
Tags: magnetic, vector potental
Share this thread:
Sep23-13, 08:24 AM
P: 4
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
Phys.Org News Partner Physics news on
Engineers develop new sensor to detect tiny individual nanoparticles
Tiny particles have big potential in debate over nuclear proliferation
Ray tracing and beyond
Sep23-13, 11:42 AM
P: 419
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:
Sep23-13, 11:45 AM
C. Spirit
Sci Advisor
WannabeNewton's Avatar
P: 5,639
What do you mean the vector potential ##A## isn't given in terms of the magnetic field ##B##? ##\nabla \times A = B## so you can picture it in terms of the usual geometric interpretation of the curl (think of the vorticity of velocity fields of fluids). The reason classically that ##A## is said to simply be a purely mathematical field (and not a physical field) is because it is not a gauge invariant quantity. I can take ##A \rightarrow A + \nabla \varphi## and I will still get the same physical magnetic field ##B## i.e. ##\nabla \times (A + \nabla \varphi) =\nabla \times A##.

Sep24-13, 12:05 AM
P: 148
How to picture the magnetic vector potental A

I've found it helpful to look at the vector potential in the Lorenz gauge -- where each component of the vector potential acts like an independent scalar potential for the corresponding current you can imagine each infinitesimal current-element in the <x, y, z> direction as a source for a corresponding 1/r A field whose vector points in the same <x, y, z> direction. What you lose, though, is the ability to see the direction of the Lorentz force by just comparing the directions of two vectors at a single point.

Register to reply

Related Discussions
What Magnetic Field Would be Generated from this Coil Layout (Picture) General Physics 3
Picture of electro-magnetic vector potential in 1+1 dimension spacetime? Classical Physics 0
Finding Curl from a vector field picture Calculus & Beyond Homework 1
Potental in a cylinder Advanced Physics Homework 0
Introductory Vector Equation Illustrated by a Moving River - Picture Included Introductory Physics Homework 3