- #1

beth92

- 16

- 0

## Homework Statement

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.)

## Homework Equations

Curl of A = B

Divergence of A = 0

## 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!