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, we need to find the induced emf in the coil and the mutual inductance between the solenoid and the coil. Let's break it down step by step.

### Step 1: Determine the Magnetic Field Inside the Solenoid
The magnetic field \( B \) inside a long solenoid is given by the formula:
\[ B = \mu_0 n i \]
where:
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