How Do I Calculate the Magnetic Force on a Coil from a Circular Ring?

[meteorologist1]

I'm stuck on the following problem:

A long thin coil of length l, cross-sectional area S, and n turns per unit length carries a current I. It is placed along the axis of a large circular ring of radius a, which is carrying a current I'. If d is the displacement of the center of the coil from the center of the ring along the coil axis, find the force on the coil as a function of d.

I'm not sure what formulas to use, and what I have to integrate to get the following result:
F = -\frac{\mu_0 II'nSa^2}{2} ((a^2 + (\frac{l}{2} - d)^2)^\frac{-3}{2} - (a^2 + (\frac{l}{2} + d)^2)^\frac{-3}{2})

Thanks.

 

[r2navlag]

Hello,first post ever, you could try to use the force from the formula

F=\int I(dl\times B)

Where B is the field from the ring