In a coil of resistance 8 Ω, the magnetic flux due to an external magnetic field varies with time as φ = 2/3(9-t²). The value of total heat produced in the coil, till the flux becomes zero, will be _____________ J. Numerical answer type. Work it out, then open the answer.

Answer: 2. e = -(dφ)/(dt) = 4/3t; flux becomes zero when 9 - t² = 0, i.e. t = 3 s. H = ∫₀³ e²/Rdt = (16)/(9 × 8)∫₀³ t² dt = 2/9 × 27/3 = 2/9× 9 So the heat produced is 2 J.

In a coil of resistance 8 Ω, the magnetic flux due to an external… | JEE Main 2022 (26 Jul, Shift 2)

Q59JEE Main 2022 · 26 JUL · SHIFT 2Medium

Magnetic Flux & Faraday's Law

In a coil of resistance $8\ \Omega$ , the magnetic flux due to an external magnetic field varies with time as $\phi = \frac{2}{3}\left(9-t^{2}\right)$ . The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $\text{J}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 2

$e = -\dfrac{d\phi}{dt} = \dfrac{4}{3}t$ ; flux becomes zero when $9 - t^2 = 0$ , i.e. $t = 3$ s.
$H = \int_0^3 \dfrac{e^2}{R}dt = \dfrac{16}{9 \times 8}\int_0^3 t^2\,dt$
$= \dfrac{2}{9} \times \dfrac{27}{3} = \dfrac{2}{9}\times 9$
So the heat produced is $2$ J.

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