Question

A current of 1.0 A is established in a tightly wound solenoid of radius 2 cm having 1000 turns/metre. Find the magnetic energy stored in each metre of the solenoid.

Answer 1

Given:-

Current through the solenoid, i = 1.0 A

Radius of the coil, r = 2 cm

Number of turns per metre, n = 1000

The magnetic energy density is given by \[\frac{B^2}{2 \mu_0}.\]

Volume of the solenoid, V = πr²l

For l = 1m, V = πr²

Thus, the magnetic energy stored in volume V is given by

\[U=\frac{B^2 \pi r^2}{2 \mu_0}\]

The magnetic field is given by

B = μ₀ni

= (4π × 10^-7) × (1000) × 1
   = 4π × 10^-4 Τ

\[U = \frac{(4\pi \times {10}^{- 4} )^2 \times 4\pi \times {10}^{- 4}}{2 \times (4\pi \times {10}^{- 7} )} \]

\[ = 8 \pi^2 \times {10}^{- 5} \]

\[ = 78 . 956 \times {10}^{- 5} \]

\[ = 7 . 9 \times {10}^{- 4} J\]