Question

Consider a small cube of volume $1m{m}^3$ at the centre of a circular loop of radius $10cm$ carrying a current of $4A$. Find the magnetic energy stored inside the cube.

Answer 1

Energy density=$\frac{B^2}{2{\mu }_0}$ where $B$=magnetic field, ${\mu }_0$magnetic permittivity

Energy stored=$\frac{B^{2}V}{2{\mu }_0}$

$=\frac{{\left(\frac{{\mu }_{0}i}{2r}\right)}^{2}v}{2{\mu }_0}=\frac{4\pi \times {10}^{-7}\times 4^2\times 1\times {10}^{-9}}{4\times {\left({10}^{-1}\right)}^2\times 2}=8\pi \times {10}^{-7}J$