(a) To find mutual inductance , it does not matter in which coil we consider current and in which 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|`=m[((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))/(b R)`.