# Magnetic Field question

1. Mar 21, 2005

### barnsworth

1) Four long, straight, parallel wires each carry current I. In plane perpendicular to the wires, the wires are at the corners of a square of side "a". Find the force per unit length on one of the wires if (a) all the currents are in the same direction, and (b) all the currents are in the opposite direction.

I got “0” for both parts (a) and (b) because when I use the right-hand rule, all B’s seem to cancel out, so F / l would invariably be 0, but this seems overly simple.

here's #2...

2) A solenoid carries “n” turns per unit length. Apply Ampere’s law to the rectangular curve shown to derive an expression for B assuming that it is uniform inside the solenoid and zero outside it.

I have no idea how to do this. I know that Ampere's Law is $$\oint B*dl = \mu*I$$, and the answer should be $$B = \frac{1}{2}\mu n I ( \frac{b}{\sqrt{b^2 + R^2}} + \frac{a}{\sqrt{a^2 + R^2}})$$. I don't even understand the diagram. Can somebody get me started on this?

thx for any help in advance.

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• ###### solenoid.GIF
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Last edited: Mar 21, 2005
2. Mar 22, 2005

### whozum

For #1:
The direction of B depends on the direction of I, so if they cancelled out for parallel then they can not cancel out for antiparallel. I'm not sure of the solution to this one but I know that fact. I'm thinking F = ILB but Im probably wrong.

For #2:
Its a closed integral, and you will be integrating along the perimeter of the rectangle with lengths a and b. if B is uniform then it is constant, and your integral simplifies to B*int{dl} . Now you have to relate the infinitesimal length 'l' to the radius of the loop R, and solve for B.

Notice in the solution you provided that the integral involves partial fraction decomposition. You can work backwards from this integral to reconstruct the integrand, and perhaps with this information the problem would be easier for you to understand.