What is the mutual inductance of a two-loop system as shown with centre separation `l`?

Options

A. `(mu_(0)pia^(4))/(8l^(3))`
B. `(mu_(0)pia^(4))/(4l^(3))`
C. `(mu_(0)pia^(4))/(6l^(3))`
D. `(mu_(0)pia^(4))/((2l^(3))`

Answer

D

Explanation

Magnetic field at the location of coil (2)produced due to coil (1)
`Bl=(mu_(0))/(4pi).(2M)/(l^(3))`
Flux linked with coil (2)
`varphi_(2)=B_(1)A_(2)=(mu_(0))/(4pi)(2i(pia^(2)))/(l^(3))xx(pia^(2))`
Also `varphi_(2)=MiimpliesM=(mu_(0)pia^(4))/(2l^(3))`