Physics - Magnetism Question with Solution | TestHub

The magnetic field inside a toroid is,

$\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{N}\mathrm{i}}{2\mathrm{\pi }\mathrm{R}}$

Flux linked with the toroid,

$\mathrm{\varphi }=\mathrm{\pi }{\mathrm{b}}^2\times \mathrm{B}\times \mathrm{N}$

Also, flux is related to self-inductance as,

$\mathrm{\varphi }=\mathrm{L}\mathrm{i}$

$\mathrm{L}=\frac{\mathrm{\varphi }}{\mathrm{i}}=\frac{{\mathrm{\mu }}_0{\mathrm{N}}^2{\mathrm{b}}^2}{2\mathrm{R}}$with$\mathrm{b}<<<\mathrm{R}$

Energy$=\frac{1}{2}\mathrm{L}{\mathrm{i}}^2=\frac{{\mathrm{\mu }}_0{\mathrm{N}}^2{\mathrm{I}}^2{\mathrm{b}}^2}{4\mathrm{R}}$