JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Electromagnetic Induction

A square loop PQRS having 10 turns, area

3.6 \times 1 0^{- 3} m^{2}

and resistance

100Ω

is slowly and uniformly being pulled out of a uniform magnetic field of magnitude

B = 0.5 T

as shown. Work done in pulling the loop out of the field in 1.0 s is
____

\times 1 0^{- 6} J

Answer: 3

Solution

Induced emf

ε = N B ℓ v

, current

i = \frac{N B ℓ v}{R}

, and the retarding force on the side in the field is

F = N B i ℓ = \frac{N ^{2} B ^{2} ℓ ^{2} v}{R}

. Work to pull the loop out a distance

ℓ

(with

v = ℓ / t

ℓ^{2} = A

W = F ℓ = \frac{N ^{2} B ^{2} A ^{2}}{R t} = \frac{( 10 ) ^{2} ( 0.5 ) ^{2} ( 3.6 \times 1 0 ^{- 3} ) ^{2}}{100 \times 1} = 3.24 \times 1 0^{- 6} J

To the nearest integer, the value is

3

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Integer answer

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