Vector potential

Does anyone know what the point of the vector potential in magnetism is? I remember it being defined in lectures, and I think it was used in a small way in a derivation of a formula for mutual inductance, but beyond that I've not seen anything interesting done with it.
Wikipedia/ hyper-physics don't have any suggestions.
Thanks

Reply 1

Willa

11

it becomes important when doing relativistic EM, where you define a 4-vector using the scalar potential and the vector potential. It also allows you to see that you can have gauge transformations in EM.

Reply 2

plmokn

OP

Thanks. With a bit of help from google, I've found out a gauge transformation is A -> A + grad(z), so we can choose to add any scalar field we like without affecting curl(A), but what on Earth does this mean physically?
Thanks
(where curl(A)=B)

Reply 3

F1 fanatic

16

plmokn

Thanks. With a bit of help from google, I've found out a gauge transformation is A -> A + grad(z), so we can choose to add any scalar field we like without affecting curl(A), but what on Earth does this mean physically?
Thanks
(where curl(A)=B)

A (vector) potential has no physical meaning or representation. The whole point of a gauge transformation (at least from my understanding) is that it makes no difference to the physical observables. So physically it has no meaning, it's just a mathematical trick.

Reply 4

plmokn

OP

Cheers.

Reply 5

Willa

11

Gauge transformations are used because certain choices for that extra term magically simplify the equations you are trying to solve, for certain physical situations that is.

Reply 6

plmokn

OP

Thanks

Reply 7

AlphaNumeric

10

Noone's said it so I'm not sure if it's because you all know it or not but the use of the vector potential means that you only have one vector to define both electric and magnetic fields as well as their equations of motion, via the Maxwell EM tensor. This, as said, has the added bonus of being Lorentz invariant in a clear manner while the Maxwell equations individually might not be as obvious.

Reply 8

plmokn

OP

I hadn't realised that (though it was probably obvious to everyone else).
Cheers

Vector potential

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