Derive the expression for the magnetic energy stored in a solenoid in terms of magnetic field B, area A and length l of the solenoid carrying a steady current 1. How does this magnetic energy per unit volume compare with the electrostatic energy density stored in a parallel plate capacitor ?

Explanation

To derive the expression for the magnetic energy stored in a solenoid in terms of the magnetic field \( B \), area \( A \), and length \( l \) of the solenoid carrying a steady current \( I \), we will follow these steps:

### Step 1: Expression for Magnetic Field in a Solenoid
The magnetic field \( B \) inside a long solenoid is given by the formula:
\[ B = \mu_0 N I \]
where \( \mu_0 \) is the permeability of free space, \( N \) is the number of turns per unit length, and \( I \) is the current flowing through the solenoid.
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