Two short magnets placed along the same axis with their like poles facing each other repel each other with a force which varies inversely as

Options

A. Square of the distance
B. Cube of the distance
C. Distance
D. Fourth power of the distance

Answer

D

Explanation

Both the magnets are placed in the field of one another, hence potential energy of dipole `(2)` is
`U_(2)=-M_(2)B_(1) cos0=-M_(2)B_(1)=M_(2)xxmu_(0)/(4pi).(2M_(1))/r^(3)`
By using `F=-(dU)/(dr)`, force on magnet `(2)` is
`F_(2)=-(dU_(2))/(dr)=-d/(dr)(mu_(0)/(4pi).(2M_(1)M_(2))/r^(3))=mu_(0)/(4pi).6(M_(1)M_(2))/r^(4)`
It can be proved `|F_(1)|=|F_(2)|=F=mu_(0)/(4pi).(6M_(1)M_(2))/r^(4)`
`implies F prop 1/r^(4)`