Find the interaction energy of two loops carrying currents `I_(1)` and `I_(2)` if both loops are shaped as circles of radii `a` and `b`, with `a lt lt b`. The loops centres are located at the same point and their planes from an angle `theta` between them.

Explanation

We can think of the smaller coil as consituting a magnet of dipole moment,
`p_(m) = pi a^(2) I_(1)`
Its direction is normal to the loop and makes and angle `theta` with the direction of the magnetic field, due to the bigger loop. This magnetic field is,
`B_(2) = (mu_(0) L_(2))/(2b)`
The interactiion energy has the magnitude,
`|W| = (mu_(0) I_(1) I_(2))/(2b) pi a^(2) cos theta`
Its sign depends on the sense of the currents.