Question

A solenoid of inductance $L$ and resistance $R$ has a soft iron core. It is connected to a battery of E.M.F $E$ as shown in the figure and allowed to attain its steady state.



At an instant, the iron core is suddenly pulled out and because of it, inductance decreases to $\frac{L}{3}$ .

The work done by an external agent in pulling out the iron core is

• A. $\frac{LE^{2}}{R^{2}}$
• B. $\frac{2 LE^{2}}{R^{2}}$
• C. $\frac{LE^{2}}{2 R^{2}}$
• D. $\frac{LE^{2}}{4 R^{2}}$

Answer 1

Answer: (A)

Flux does not change suddenly.
$\therefore \, L_{1}I_{1}=L_{2}I_{2}$
$\therefore \, W=U_{2}-U_{1}=\frac{1}{2}\times \left(\frac{L}{3}\right)\times \left(\frac{3 E}{R}\right)^{2}-\frac{1}{2}\times L\times \left(\frac{E}{R}\right)^{2}$
$=\frac{3 E^{2} L}{2 R^{2}}-\frac{E^{2} L}{2 R^{2}}=\frac{E^{2} L}{R^{2}}$