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 a ans negligible self-inductance lies in the `y-z` plane with its centre 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 centre of the loop is much greater than a .

Explanation

Magnetic field to magnet at the position of loop
`B=(mu_(0))/(4pi)(2M)/(x^(3))` , toward right
Flux through loop
`phi=BA=mu_(0)/(4pi).(2M)/(x^(3)).pia^(2)=(mu_(0)Ma^(2))/(2x^(3))`
Induced current in the loop
`I=(e)/(R)=(3mu_(0)Ma^(2)v)/(2x^(4)R)` , anticlockwise as seen from magnet
Dipole moment induced in the loop
`M_(0)=IA=(3mu_(0)Ma^(2)v)/(2x^(4)R).pir^(2)=(3mu_(0)Ma^(4)v)/(2x^(4)R)`
Force between dipoles,
`F=(mu_(0))/(4pi)(6MM_(0))/(x^(4))=(mu_(0))/(4pi)(6M)/(x^(4)).(3mu_(0)Ma^(4)v)/(2x^(4)R)`
`=(9)/(4)(mu_(0)^(2)M^(2)a^(4)v)/(x^(8)R)`