Electromagnetic Induction

JEE Main level, numerical answer, medium

19 of 153

Question 19 of 153

In a coil of resistance 8Ω8\Omega, the magnetic flux due to an external magnetic field varies with time as ϕ=23(9−t2)\phi =\dfrac{2}{3}\left(9-{t}^{2}\right). The value of total heat produced in the coil, till the flux becomes zero, will be _____ JJ.

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Answer: 2

It is given that magnetic flux ϕ=23(9−t2)\phi =\dfrac{2}{3}\left(9-{t}^{2}\right)
For magnetic flux to be zero 0=23(9−t2)⇒t=3s0=\dfrac{2}{3}\left(9-{t}^{2}\right)\Rightarrow t=3s
According to Faraday's law of electromagnetic induction,
ϵ=−dϕdt=−23(0−2t)=4t3\epsilon =-\dfrac{d\phi }{dt}=-\dfrac{2}{3}\left(0-2t\right)=\dfrac{4t}{3}
Heat produced from 00 to 3s3s,
H=∫03ϵ2Rdt=∫0316t29×8dt=2JH={\int }_{0}^{3}\dfrac{{\epsilon }^{2}}{R}dt={\int }_{0}^{3}\dfrac{16{t}^{2}}{9\times 8}dt=2J

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