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 (L/3) . The work done by an external agent in pulling out the iron core is

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. Question

At an instant, the iron core is suddenly pulled out and because of it, inductance decreases to (L/3) . The work done by an external agent in pulling out the iron core is (A) (LE2/R2) (B) (2 LE2/R2) (C) (LE2/2 R2) (D) (LE2/4 R2)

Tardigrade Admin · Accepted Answer

Flux does not change suddenly. ∴ L1I1=L2I2 ∴ W=U2-U1=(1/2)× ((L/3))× ((3 E/R))2-(1/2)× L× ((E/R))2 =(3 E2 L/2 R2)-(E2 L/2 R2)=(E2 L/R2)

$\frac{L E ^{2}}{R ^{2}}$

$\frac{2 L E ^{2}}{R ^{2}}$

$\frac{L E ^{2}}{2 R ^{2}}$

$\frac{L E ^{2}}{4 R ^{2}}$

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

R2LE2​

R22LE2​

2R2LE2​

4R2LE2​

Flux does not change suddenly. ∴L1​I1​=L2​I2​ ∴W=U2​−U1​=21​×(3L​)×(R3E​)2−21​×L×(RE​)2 =2R23E2L​−2R2E2L​=R2E2L​

$\frac{L E ^{2}}{R ^{2}}$

$\frac{2 L E ^{2}}{R ^{2}}$

$\frac{L E ^{2}}{2 R ^{2}}$

$\frac{L E ^{2}}{4 R ^{2}}$

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