Question

The approximate formula expressing the formula of mutual inductance of two coaxial loops of the same redius `a` when their centers are separated by a distance `l` with `l gt gt a` is
A. `(1)/(2)(mu_(0)pa^(4))/(l^(3))`
B. `(1)/(2)(mu_(0)a^(4))/(l^(2))`
C. `(mu_(0))/(4pi)(pia^(4))/(l^(2))`
D. `(mu_(0))/(pi)(a^(4))/(l^(3))`

Answer 1

Correct Answer - A
Let `I`=current in once loop. This magnetic flux at the centre of the other co-axial loop at a distance `l` from the centre of the first loop is
`B=(mu_(0))/(4pi)(2I.pia^(2))/((a^(2)+l^(2)))^(3//2))`
where `p_(m)=I.pia^(2)`
=magnetic moment of loop.
the flux through the other loop is
`phi_(12)=Bpi a^(2)`
`=(mu_(0))/(4pi).(2pia^(2)I)/(a^(2)+l^(2))^(3//2)pia^(2)`
or `(phi_(12))/(I)=(mu_(0))/(4pi).(2pi^(2)a^(4))/(2(a^(2+l^(2)))^(3//2))`
`=(phi_(0)pia^(4))/(2(a^(2)+l^(2))^(3//2)`
:.`mu_(12=M_(12)I`
:. `M_(12)=(phi_(12))/(I)=(1)/(2)(mu_(0)pia^(4))/(l^(3))`
:. `a lt lt 1`.