The current in a long solenoid of radius R and having n turns per unit length is given by `i= i_0 sin omega t`. A coil having N turns is wound around it near the centre. Find (a) the induced emf in the coil and (b) the mutual inductance between the solenoid and the coil.

Explanation

To solve the problem step by step, we will address both parts of the question: (a) finding the induced emf in the coil and (b) calculating the mutual inductance between the solenoid and the coil.

### Part (a): Finding the Induced EMF in the Coil

1. **Identify the Magnetic Field in the Solenoid**:
The magnetic field \( B \) inside a long solenoid is given by the formula:
\[
B = \mu_0 n i
...