Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance
Energy Stored in Magnetic Field
Just as capacitor stores electric energy, an inductor can store magnetic energy. To see this consider an L-R circuit in which a current $I_0$ is established. If the switch is thrown to the position such that the battery gets disconnected from the circuit at $t=0$, the current in the circuit would decay. As the inductor provides back emf, the circuit is described by
 
\begin{displaymath}L\frac{dI}{dt}+ IR =0\end{displaymath}
  With the initial condition $I=I_0$, the solution of the above is
 
\begin{displaymath}I = I_0\exp(-Rt/L)\end{displaymath}
  As the energy dissipated in the circuit in time $dt$ is $RI^2dt$, the total energy dissipated from the time the battery is disconnected is
 
\begin{displaymath}U = \int_0^\infty RI^2 dt = \int_0^\infty RI_0^2\exp(-2Rt/L)dt = \frac{1}{2}LI_0^2\end{displaymath}
   
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