# Homework Help: Magnetic Vector Potential help

1. Mar 16, 2012

### beth92

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

For the magnetic field B=k/s3 z determine the magnetic vector potential A. For simplicity, assume that A does not have a component in the s direction.

(I don't know if this is relevant but this was a follow up question to one in which I was required to find the induced current for a bar moving along a semicircular loop of wire - like a slide wire generator bent into a semicircular shape - and then the torque on the bar due to the magnetic force and then the position ∅ at which the bar comes to rest.)

2. Relevant equations

Curl of A = B

Divergence of A = 0

3. The attempt at a solution

The z component of the curl of A in cylindrical coordinates is:
1/s[d(sA)/ds - d(As)/d∅]

The B field we are considering has only a z component so the s and components of the curl of A can be disregarded. Also, we are told in the problem that As = 0 so the only surviving term, equal to B, is:

1/s d(A)/ds = k/s3

Separating the variables:

∫ d(sA) = ∫ (k/s2) ds

After integration, we get:

A = -k/s2 + C/s

Where C is the integration constant.

This is as far as I got....I'm not sure how how to find out what C is. Any tips would be appreciated!

2. Mar 16, 2012

### tiny-tim

hi beth92!

vector potential is like scalar potential …

only the potential difference matters, so you can add any constant vector you like! :tongue2: