Question

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

Answer 1

$i=1.0A,r=2cm,n=1000turn/m$
magnetic energy stored $=\frac{B^{2}V}{2{\mu }_0}$
where $B$-magnetic field, $V$- Volume of solenoid
$=\frac{{\mu }_0{n}^2{i}^2}{2{\mu }_0}\times \pi r^{2}h=\frac{4\pi \times {10}^{-7}\times {10}^6\times 1\times \pi \times 4\times {10}^{-4}\times 1}{2}$ ($h=1m$)
$=8{\pi }^2\times {10}^{-5}=7.9\times {10}^{-4}J$