Two current carrying coil having radius 'r' are seperated by distance 'd' as shown in diagram. If `rlt ltd`. Then find the force between two ring. Current in both the ring is clockwise and equal to i.

Options

A. `(6mu_(0))/(4pi)(i^(2)pi^(2)r^(4))/(d^(4))`
B. `(mu_(0))/(4pi)(i^(2)pi^(2)r^(4))/(d^(4))`
C. `(3mu_(0))/(4pi)(i^(2)pi^(2)r^(4))/(d^(4))`
D. `(mu_(0))/(2pi)(i^(2)pi^(2)r^(4))/(d^(4))`

Answer

A

Explanation

`f=mu(dB)/(dx)`
`B=(2mu_(0)M)/(4pid^(3)) implies (dB)/(dd)=-(6mu_(0)M)/(4pid^(4))`
`F=M_(1)M_(2)[-(6mu_(0))/(4pid^(4))]=-(6)/(4pi)(mu_(0)M_(1)M_(2))/(d^(4))`
`-(6mu_(0)(pir^(2)i)(pi^(2)i))/(4pid^(4))`