(b) The coefficient of mutual induction is given by M=
µ0N1N2A
I
⋅⋅⋅⋅⋅⋅⋅(i) where, µ0 is the permeability of free space, N1 is the number of turns in primary coil, N2 is the number of turns in secondary coil, A is the common area of cross-section and l is the length of coils. Thus, for toroid the Eq. (i) is given as M=
µ0N⋅N⋅πR2
2πr
=
µ0N2R2
2r
[
∵N1=N2=N
A=πR2
l=2πr
] where, R is the major radius and r is the minor radius.