Repulsive Force on Current Carrying Wire

[erok81]

Homework Statement

I have a rectangular conductor with a current A flowing through. I am trying to find the repulsive force acting on a 1.0cm piece at the center of the conductor.

Homework Equations

Here is what I've tried with no success. The way I am picturing this is by the attached image.

F=Il X B
B=mu0/2pi * I/d

The Attempt at a Solution

Just about all of the formulas I have, and have used, always contain a d from the wire. This is why I am stuck. I really just don't see how to set up the problem.

My current idea is this...but I am not the best at limiting cases so I don't know if this is a legal move.

For a long wire with a point d away from the wire the magnetic field is:

$$B_wire=\frac{\mu_0}{2\pi}*\frac{I}{d}$$

Can I take the limiting case where d goes to zero (i.e. inside the conductor) and end up with:

$$B_wire=\frac{\mu_0}{2\pi}*I$$

I was thinking if I could find the field inside the conductor then use F=Il X B and solve for F I'd be in business.

I have a feeling that I'm not even close those.

Any pointers?

I did find this, http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html#c1, but it's using two wires where I only have one. So I don't think this method will work either?

 

[Redbelly98]

Homework Equations

F=Il X B
B=mu0/2pi * I/d

The Attempt at a Solution

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I did find this, http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/wirfor.html#c1, but it's using two wires where I only have one. So I don't think this method will work either?

For this problem, it looks like you do pretty much have two long parallel wires. The fact that they are connected together at their ends will not significantly influence the force in the middle of the wires.

I interpret the question as asking for the force on a 1 cm length of wire, in the middle of either one of the wires. The square section you indicated in your figure is rather misleading or not quite relevant to thinking about what is going on.

It looks like the first two equations you wrote will suffice to solve this problem.