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ELECTROMAGNETIC INDUCTION — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsELECTROMAGNETIC INDUCTION2 Marks
Question
Obtain expression for energy required to establish electric current I in a coil having self inductance L.
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Obtain expression $U_B=\frac{1}{2} L I ^2$ for magnetic energy stored while establishing current I in coil having self inductance L.
✓

Answer

→Self induced emf in a coil having self inductance L is
$\varepsilon=- L \frac{d I }{d t}$
This self induced emf opposes the change in current taking place in coil. Hence it is also called Back emf.
→Physically, self inductance plays the role of inertia in electricity.
→Work is required to be done against back emf to establish electric current in coil. This energy spent gets stored in form of magnetic energy $U _{ B }$ in the coil.
→Suppose, time rate of work done to establish current I in coil at any instant is $\frac{d W}{d t}$ then
$\begin{aligned}
\frac{d W}{d t} & =|\varepsilon| I \text { (neglecting ohmic loss.) } \\
\therefore \quad \frac{d W}{d t} & = L I \frac{d I }{d t} \text { (from equation (1)) }
\end{aligned}$
→Total work done to establish current I
$\begin{aligned}
W & =\int_0^1 d W=\int_0^1 LI d I = L \int_0^1 I d I \\
\therefore \quad W & =\frac{1}{2} L I ^2
\end{aligned}$
→Energy spent in doing this work gets stored in form of magnetic energy in the coil.
$\therefore$ Magnetic potential energy $U _{ B }=\frac{1}{2} LI ^2 \ldots$

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