An infinitesimal bar magnet of dipole moment $M$ is pointing and moving with speed $v$ in the $x-$direction. A closed circular conducting loop of radius $\alpha$ and negligible self-inductance lies in the $y-z$ plane with its center at $x = 0$ and its axis coinciding with $x-$axis. Find the force opposing the motion of the magnet, if the resistance of the loop is $R$. Assume that the distance $x$ of the magnet from the center of the loop is much greater than $\alpha$.

The magnetic field of a bar magnet at its axial point, distance x from its center is given by, 

B=μ04π2Mx3

Magnetic flux linked with the loop 

ϕ=BA=μ04π2Mx3πa2

The induced emf in the loop due to motion of magnet

E=-dϕdt=μ04π6πMa2x4dxdt=μ04π6πMa2x4v

The induced current in the loop, 

I=ER=μ04π6πMa2Rx4v

The induced magnetic moment in the coil 

=I×A=μ04π6π2Ma4Rx4v

The magnetic force between two magnetic dipole is given by 

F=μ04π6M1M2x4

Hence opposing force 

F=94μ02M2a4Rx8v