Magnetic Vector Potential


by beth92
Tags: curl, magnetic field, magnetic potential, magnetism, potential, vector potential
beth92
beth92 is offline
#1
Mar16-12, 12:35 AM
P: 10
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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tiny-tim
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#2
Mar16-12, 06:24 AM
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tiny-tim's Avatar
P: 26,167
hi beth92!

vector potential is like scalar potential

only the potential difference matters, so you can add any constant vector you like!
i'd add 0


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