A conducting circular loop of area $1.0 \mathrm{~m}^{2}$ is placed perpendicular to a magnetic field which varies as $\mathrm{B}=\sin (100 \mathrm{t})$ Tesla. If the resistance of the loop is $100 \Omega$, then the average thermal energy dissipated in the loop in one period is \_\_\_\_ J.

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Electromagnetic Induction

A conducting circular loop of area

1.0 m^{2}

is placed perpendicular to a magnetic field which varies as

B = sin (100 t)

Tesla. If the resistance of the loop is

100Ω

, then the average thermal energy dissipated in the loop in one period is ____ J.

(A) $\frac{π}{2}$
(B) $2 π$
(C) $π$ ✓ Correct
(D) $π^{2}$

Answer: (C)

Solution

The flux is

ϕ = B A = sin (100 t)

, so the induced emf is

ε = - \frac{d ϕ}{d t} = - 100 cos (100 t)

and the instantaneous power is

\frac{ε ^{2}}{R} = \frac{1 0 ^{4} cos ^{2} ( 100 t )}{100} = 100 cos^{2} (100 t)

. Over one period the mean of

cos^{2}

\frac{1}{2}

, and with

T = \frac{2 π}{100} = \frac{π}{50} s

the energy dissipated is

⟨ P ⟩ T = 50 \times \frac{π}{50} = π J

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option

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