# Magnetic Vector Potential

by beth92
Tags: curl, magnetic field, magnetic potential, magnetism, potential, vector potential
 P: 8 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!
 PF Patron HW Helper Sci Advisor Thanks P: 25,497 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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