Electromagnetic Induction

JEE Main level, single correct, medium

35 of 153

Question 35 of 153

At time t=0t=0 magnetic field of 1000Gauss1000Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500Gauss,500Gauss, in the next 5s,5s, then induced EMFEMF in the loop is:

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Answer: (A) 56μV56\mu V

ϵ=∣−dϕdt∣=∣−AdBdt∣\epsilon =\left|-\dfrac{d\phi }{dt}\right|=\left|-\dfrac{AdB}{dt}\right|
ϵ=∣−ΔϕΔt∣=∣AΔBΔt∣\epsilon =\left|-\dfrac{\Delta \phi }{\Delta t}\right|=\left|\dfrac{A\Delta B}{\Delta t}\right|
=(16×4−4×2)(1000−500)5×10−4×10−4=\left(16\times 4-4\times 2\right)\dfrac{\left(1000-500\right)}{5}\times {10}^{-4}\times {10}^{-4}
=56×5005×10−8=56×10−6V=56\times \dfrac{500}{5}\times {10}^{-8}=56\times {10}^{-6}V

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