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Magnetic Vector Potential 
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#1
Mar1612, 12:35 AM

P: 10

1. The problem statement, all variables and given/known data
For the magnetic field B=k/s^{3} 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(A_{s})/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 A_{s} = 0 so the only surviving term, equal to B, is: 1/s d(A_{∅})/ds = k/s^{3} Separating the variables: ∫ d(sA_{∅}) = ∫ (k/s^{2}) ds After integration, we get: A_{∅} = k/s^{2} + 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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