JEE Main · 2005 · 08 May 2005 · Offline · Electromagnetic Induction

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One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field

B

is perpendicular to the plane of the figure. if each tube moves towards the other at a constant speed V,

then the emf induced in the circuit in terms of

B

ℓ

and V where

ℓ

is the width of each tube will be

(A) $B ℓ V$
(B) $- B ℓ V$
(C)zero
(D) $2 B ℓ V$ ✓ Correct

Answer: (D)

Solution

Each U-tube acts as a sliding conductor of width

ℓ

moving at speed

V

, and both approach each other, so the enclosed loop shrinks at the combined rate

\frac{d A}{d t} = 2 ℓ V

. The induced emf is

ε = B \frac{d A}{d t} = 2 B ℓ V

, the factor of two coming from both tubes contributing to the change in area.

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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