Question

Find the energy stored in the magnetic field inside a volume of $1.00m{m}^3$ at a distance of $10.0cm$ from a long wire carrying a current of $4A$.

Answer 1

Current flowing through the wire, $i=4.00A$

Volume of the region, $V=1m{m}^3$

Distance of the region from the wire, $d=10cm$ $=0.1m$

Magnetic field due to the current carrying straight wire, $B=\frac{{\mu }_{0}i}{2\pi r}$

Now Magnetic energy stored $=\frac{B^2}{2{\mu }_0}\times V$

$\begin{array}{c}=\frac{{{\mu }_0}^2{i}^2}{4\pi r^2}\times \frac{1}{2{\mu }_0}\times V\\ =\frac{\left(4\pi \times {10}^{-7}\right)\times 16\times 1\left(1\times {10}^{-9}\right)}{4\times 1\times {10}^{-2}\times 2}\\ =\frac{8}{\pi }\times {10}^{-14}J\\ =2.55\times {10}^{-14}J\end{array}$