Consider a long solenoid of radius `R` which has `n` turns per unit length. A time dependent current `I=I_(0) sin omegat` flows solenoid, magnitude of electric field at a perpendicular distance `rltR`, from the axis of symmetry of solenoid is found to be `E=(alpha)/4omegamu_(0) nI_(0)r cosomegat`, where `alpha` is pure number and `mu_(0)` is permability of free space. Find `alpha`

Explanation

To find the value of \(\alpha\) in the given expression for the electric field \(E\) around a long solenoid, we can follow these steps:

### Step 1: Understanding the Problem
We have a long solenoid with radius \(R\) and \(n\) turns per unit length. A time-dependent current \(I = I_0 \sin(\omega t)\) flows through the solenoid. We need to find the value of \(\alpha\) in the expression for the electric field at a distance \(r < R\) from the axis of the solenoid.

### Step 2: Magnetic Field Inside the Solenoid
The magnetic field \(B\) inside a long solenoid is given by:
\[
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