Physics - EMI/AC Question with Solution | TestHub

The magnetic field exist in the space between the cylinder elsewhere it is zero. The energy stored per unit volume is $\frac{1}{2{\mu }_0}{\left(\frac{{\mu }_0\mathrm{l}}{8\pi \mathrm{r}}\right)}^2=\frac{{\mu }_0{\mathrm{I}}^2}{8{\mu }^2{\mathrm{r}}^2}$ The energy in a cylindrical shell of length $l$ and radius $r$ and thickness dr is

$$\begin{array}{rlr}& \int {\mathrm{du}}_{\mathrm{B}}={\int }_{\mathrm{a}}^{2\mathrm{a}}\frac{{\mu }_0{1}^2}{8{\pi }^2{\mathrm{r}}^2}2\pi \mathrm{rl}\cdot \mathrm{dr}{\mathrm{U}}_{\mathrm{B}}=\frac{{\mu }_0{1}^2}{4\pi }\ln (2)=\frac{1}{2}{\mathrm{Ll}}^2\frac{\mathrm{L}}{1}=\frac{{\mu }_0}{2\pi }\ln (2)& \end{array}$$

$$=\frac{4{\mu }_0\ln 2}{8\pi }=\frac{{\mu }_0}{8\pi }\ln 16$$