Mar16-12, 12:35 AM
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!
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