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JEE Main 202329 JanuaryMorning Shift
Exam
JEE Main
Year
2023
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2023 · 29 January · Morning Shift · Physics · Electromagnetic Induction

A certain elastic conducting material is stretched into a circular...

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B=0.8TB = 0 . 8T. When released the radius of the loop starts shrinking at a constant rate of 2cms–12cm{s}^{– 1}. The induced emf in the loop at an instant when the radius of the loop is 10cm10cm will be ______ mVmV.

Correct answer

0

Step-by-step solution

According to the Faraday's law of electromagnetic induction, the emf induced in a conducting loop is given by, e=−dϕdte = - \dfrac{d ϕ}{d t}, here, tt is time and ϕ=BAϕ = BA is magnetic flux.

Here, e=∣dϕdt∣=d(BA)dt=Bd(πr2)dte = \left|\dfrac{d ϕ}{d t}\right| = \dfrac{d \left(BA\right)}{d t} = B\dfrac{d \left(\pi{r}^{2}\right)}{d t}

=Bπ(2rdrdt)=2×π×0.1×0.8×2×10−2= B\pi\left(2r\dfrac{d r}{d t}\right) = 2 \times \pi \times 0 . 1 \times 0 . 8 \times 2 \times {10}^{- 2}

≈10mV\approx 10mV (rounded off)

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