Question

Consider a toroid of circular cross-section of radius $b$ , major radius $R$ much greater than minor radius $b$ , (see diagram) find the total energy stored in magnetic field of toroid -

• A. $\frac{B^{2} \pi ^{2} b^{2} R}{2 \mu _{0}}$
• B. $\frac{B^{2} \pi ^{2} b^{2} R}{4 \mu _{0}}$
• C. $\frac{B^{2} \pi ^{2} b^{2} R}{8 \mu _{0}}$
• D. $\frac{B^{2} \pi ^{2} b^{2} R}{\mu _{0}}$

Answer 1

Answer: (D)

$B=\frac{\mu _{0} N i}{2 R}$
$\phi=\pi b^{2}\times B\times N$
$\phi=Li$
$L=\frac{\phi}{i}=\frac{\mu _{0} N^{2} b^{2}}{2 R}$ , with $ \, b < < < R$
$E=\frac{1}{2}Li^{2}=\frac{\mu _{0} N^{2} i^{2}}{4 R}b^{2}$