Name: Magnetic Energy Density Stored in a Solenoid
Uploaded: 2019-07-19
Duration: 6 min 18 s
Description: The fourth state of matter is plasma and it is superheated matter. Where can we store this kind of energy? In a solenoid! Tune in to learn more about energy...

Question

Derive the expression for the energy stored in an inductor of coefficient of self inductance $L$ carrying current $I_{0_{}}$

Accepted Answer

Given the inductance of the inductor= $L$ .

The current in the inductor = $I_{0}$

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let $dw$ be the small work done during a small interval of time $dt$

so $dw = P . dt$ ( $P$ = power, rate of doing work)

= $ε I_{0} dt$ ( power = voltage (emf) x current

But $ε = - L \frac{{di}_{0}}{dt}$ ( in case of an inductor)

therefor $dw = L \frac{{dI}_{0}}{dt} dt = {LI}_{0} {dI}_{0}$

Total work done in increasing the current from zero to a value $I$

$w = \int_{0}^{t} dw = \int_{0}^{i} {Li}_{0} {dI}_{0} = L \int_{0}^{i} i_{0} {dI}_{0} = \frac{1}{2} {LI}_{0}^{2}$

This is the required expression for the energy stored in an inductor

Derive the expression for the energy stored in an inductor of coefficient of self inductance $L$ carrying current $I_{0_{}}$

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Derive the expression for the energy stored in an inductor of coefficient of self inductance L carrying current I0

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Derive the expression for the energy stored in an inductor of coefficient of self inductance $L$ carrying current $I_{0_{}}$