A solenoid of inductance L and resistance R has a soft iron core....

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.

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

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

At an instant, the iron core is suddenly pulled out and because of it, inductance decreases to

\dfrac{L}{3}

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

Options

A $\dfrac{LE2}{R2}$
B $\dfrac{2{LE}^{2}}{R2}$
C $\dfrac{LE2}{2R^{2}}$
D $\dfrac{LE2}{4R^{2}}$

Correct answer

A. $\dfrac{LE2}{R2}$

Step-by-step solution

Flux does not change suddenly.

∴ {L}_{1}{I}_{1} = {L}_{2}{I}_{2}

∴ W = {U}_{2} - {U}_{1} = \dfrac{1}{2} \times \left(\dfrac{L}{3}\right) \times \left(\dfrac{3E}{R}\right)^{2} - \dfrac{1}{2} \times L \times \left(\dfrac{E}{R}\right)^{2}

= \dfrac{3E^{2}L}{2R^{2}} - \dfrac{E^{2}L}{2R^{2}} = \dfrac{E^{2}L}{R2}

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The… JEE Advanced 2026 A 30 cm long solenoid has 10 turns per cm and area of 5 cm ^2 . The current through the… JEE Main 2026 A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B… JEE Main 2026 An inductor of inductance 10 mH having resistance of 100\,Ω is connected to battery of… JEE Main 2026 A metal rod of length L rotates about one end at origin with a uniform angular velocity ω… JEE Main 2026 A circular loop of radius 20 cm and resistance 2\ Ω is placed in a time varying magnetic… JEE Main 2026 In the given circuit below inductance values of L_1 , L_2 and L_3 are same. The magnetic… JEE Main 2026 A circular current loop of radius R is placed inside square loop of side length L (L >>… JEE Main 2026 Full Electromagnetic Induction list All NTA Abhyas JEE Main PYQs