Question

Consider a small cube of volume 1 mm³ at the centre of a circular loop of radius 10 cm carrying a current of 4 A. Find the magnetic energy stored inside the cube.

Answer 1

Given:-

Current in the loop, i = 4 A

Radius of the loop, r = 10 cm = 0.1 m

Volume of the cube, V = 1 mm³ = 1 × 10^-9m

Magnetic field intensity at the centre of the circular loop:-

\[B = \frac{\mu_0 i}{2r}\]

\[ = \frac{(4\pi \times {10}^{- 7} ) \times 4}{2 \times 0 . 1}\]

\[ = 8\pi \times {10}^{- 6} T\]

Magnetic energy density = \[\frac{B^2}{2 \mu_0}\]

otal energy stored in volume V:-

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

\[= \frac{(8\pi \times {10}^{- 6} )^2 \times (1 \times {10}^{- 9} )}{(4\pi \times {10}^{- 7} ) \times 2}\]

\[ = 8\pi \times {10}^{- 14} J\]