If a current flowing in a coil is reduced to half of its initial value, the relation between the new energy…

If a current flowing in a coil is reduced to half of its initial value, the relation between the new energy $\left(\mathrm{E}_2\right)$ and the original energy $\left(E_1\right)$ stored in the coil will be
  1. $E_2=\frac{E_1}{4}$
  2. $E_2=\frac{E_1}{2}$
  3. $\mathrm{E}_2=\mathrm{E}_1$
  4. $\mathrm{E}_2=\mathrm{4E}_1$

Solution

$\begin{aligned} & E_1=\frac{1}{2} Li_1^2, \quad E_2=\frac{1}{2} Li_2^2 \\ & \therefore \frac{E_2}{E_1}=\left(\frac{I_2}{I_1}\right)^2=\left(\frac{1}{2}\right)^2=\frac{1}{4} \\ & \therefore E_2=\frac{E_1}{4}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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