Figure. shows two concentric coplanar coils with radii `a` and `b(alt ltb)`. A current `I = 2t` flows in the smaller loop. Neglecting self-inductance of the larger loop,
a. find the mutual inductance of the two coils,
b. find the emf induced in the larger coil,
c. if the resistance of the larger loop is `R`, find the current in it as a function of time.

Explanation

a. To find mutual inductance, it does not matter in which coil we consider current and in which coil flux is calculated (reciprocity theorem).Let current `i` be flowing in the larger
coil. Magnetic field at the centre `= (mu_(0)i)/(2b)*`
Flux through the smaller coil `= (mu_(0)i)/(2b) pia^(2)`
`:. M = (mu_(0))/(2b) pia^(2)`
b. |emf induced in larger coil|` = [((di)/(dt))` in smaller coil]
`= (mu_(0))/(2b) pia^(2)(2) = (mu_(0)pia^(2))/(b)`
c. current in the larger coil `= (mu_(0)pia^(2))/(bR)*`