Force on small wire segment in ring

[unscientific]

Homework Statement

Part (a): Describe what happens to current when ring contracts
Part(b): Find how much energy is stored, changing per unit time and rate of mechanical work being done
Part (c): Show the pressure is given by:
Part (d): Why is the force on a small wire segment not BIL?

Homework Equations

The Attempt at a Solution

Part(d)

I tried a geometric reasoning, saying the horizontal components cancel out. So the net force is $$2Fcos(\frac{\theta}{2}) = 2F\sqrt{1-(\frac{L}{2r})^2} = BIL\sqrt{4 - (\frac{L}{r})^2}$$

Somehow I don't think that's the answer they are looking for..

 

[unscientific]

bumpp

 

[TSny]

If you take L << r for a segment of wire, then you can consider it as essentially straight when calculating the force on the segment.

I think the purpose of the problem is to show that the magnetic force on the segment is not BIL, where B is the field inside the solenoid. This can be surprising since BIL is the usual expression for the force.

As the solenoid expands in radius, the energy supplied by the current source goes somewhere. If you can identify where it goes, then you can use energy concepts to deduce the amount of magnetic force on a segment of wire.