Question

Figure shows tow concentric coplanar coils with radii a and b `(a lt lt b)`. A current i=2t flows in the smaller loop. Neglecting self inductance of larger loop

(a) Find the mutual inductance of 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.

Answer 1

(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)`.