How to Calculate the Mutual Force Between Two Coils?

[emlio]

Homework Statement

In a compact cicrcualr coil "A" (radius R= 25cm),formed by N=150 loops of wire, flows I=10A current.
There's another compact circular coil "B" over "A"(radius r= 1.5 cm, loops n= 30) coaxial with "A" distant X ,in which i= 4A flows .
in the same direction of "I" (look at the image).

Calculate the mutual force between the two coils, and is it repulsive or attractive ?
Calculate X value when the force is Maximum.

http://img179.imageshack.us/img179/7660/bobinacn6.jpg

HELP ME I DON'T KNOW HOW TO SOLVE IT...sorry for the translation English isn't my mother tongue.

Homework Equations

The Attempt at a Solution

 

[Meir Achuz]

The problem is very complicated if done exactly, because you would need B off the axis of one of the coils. Assuming R=1.5 cm is small enough, you can approximate the smaller coil by a magnetic dipole. Then the force on the larger coil is not hard to calculate.