At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly… | JEE Main 2020 (8 Jan, Shift 1)

Q67JEE Main 2020 · 8 JAN · SHIFT 1Easy

Magnetic Flux & Faraday's Law

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loop is:

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Answer: (c)

Loop area = rectangle minus the two triangular cut-outs (base 4 cm, height 2 cm each).
$A = 16\times 4 - 2\times\frac{1}{2}\times 4\times 2 = 64 - 8 = 56$ cm $^{2} = 56\times 10^{-4}$ m $^{2}$
$\Delta B = 1000 - 500 = 500$ G $= 0.05$ T, $\frac{\Delta B}{\Delta t} = \frac{0.05}{5} = 0.01$ T/s
$e = A\frac{\Delta B}{\Delta t} = 56\times 10^{-4}\times 0.01 = 56\times 10^{-6}$ V
So the answer is (c) 56 $\mu$ V.

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