Question

Write down an expression for the energy stored in the magnetic field of an inductor when the current is i. Use this expression to derive an equation for the magnetic energy density of a solenoid. A resistor, inductor and capacitor all store energy through different mechanisms. Briefly describe the way that each of these components stores energy

Answer 1

Energy stored in the inductor, E = (1/2)Li²

Magnetic energy density of a solenoid, = Energy/volume = $\frac{\frac{1}{2}Li^{2}}{Al}$

eta B = B^2/2mu B = mu Ni/l L = mu N^2A/l eta B = /(mu N^2A/l * B^2 l^2/mu^2 N^2)/Al /Li^/Al eta B

or    $\eta _{B}= \frac{\frac{1}{2}\left ( \frac{\mu N^{2}A}{l}*\frac{B^{2}l^{2}}{\mu ^{2}N^{2}} \right )}{Al}$              .........................( As $L=\frac{\mu N^{2}A}{l}$       and $B=\frac{\mu Ni}{l}$ )

or $\eta _{B}=\frac{B^{2}}{2\mu }$

24) energy is stored in resistor in the form of heat, energy is stored in inductor in the form of magnetic flux and energy is stored in capacitor in the form electric potential energy du to stored charge.