# Force between two current-carrying loops

1. The problem statement, all variables and given/known data
Consider two circular, parallel, coaxial loops which are almost in contact. They are separated by 1.20mm, have 13.6cm as radius each. Both loops carry a current of I = 127A but in opposite directions. Find the magnetic force that the top loop exerts on the bottom loop.

2. Relevant equations

3. The attempt at a solution
I tried to "readapt" the force between two parallel wires, to be able to use it for two loops, in which we would have $F = BIl = 2\pi BIr$. Then, I used the formula for the field that a loop exerts on its axis, but now I’m doubting if this is true as actually this field is not felt by the other current loop. Now I am stuck on which way to calculate the force that one loop exerts on the other. I was thinking of finding the force exerted on one small piece of the circle dr and then try to integrate in order to find the total force.

Thank you for your time and patience.

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