Question

A solenoid stores $0.1\text{J}$ of energy when connected in a circuit, with a cell and a resistor in steady state. If an iron core of relative permeability $1200$ is inserted in it, without changing anything else, how much energy will it store in the steady state?

• A. $120\text{J}$
• B. $12\text{J}$
• C. $1200\text{J}$
• D. $0.12\text{J}$

Answer 1

The correct option is A $120\text{J}$

The energy stored in the inductor is,

$U=\frac{1}{2}L{i}^2$

$\Rightarrow U\propto L$

Also, for a solenoid, inductance,

$L=\mu n^2\pi R^{2}l$

$\Rightarrow L\propto \mu$

So, $U\propto \mu$

$\therefore \frac{U_1}{U_2}=\frac{{\mu }_1}{{\mu }_2}$

$\Rightarrow \frac{0.1}{U_2}=\frac{{\mu }_0}{{\mu }_r{\mu }_0}=\frac{1}{1200}$

$\Rightarrow U_2=120\text{J}$

Hence, option $\left(A\right)$ is the correct answer.