I came across a scenario in which a coil having a radius $r$ is placed co axially to another coil having radius $R$. They have some non zero finite distance between their centers. If some finite current is passed through the coil of radius $r$,(provided that $r<<R$) what is the magnetic flux linked with the larger coil due to the magnetic field produced by the smaller coil.
I tried to equate the flux density to solid angle but realized that the dipole did not produce magnetic field which was symmetrical in all directions, i.e. the flux density was not constant in every direction at a given constant distance from the dipole.
I also tried to integrate the magnetic flux by taking the product of magnetic field at every point in the plane of the larger coil, but found it too complex to compute.
Is their any way to form a mathematical model of this situation which is easy to compute as well as to visualize? Your opinions are welcome...