Electromagnetic Induction

JEE Main level, single correct, medium

61 of 153

Question 61 of 153

A coil of circular cross-section having 1000 turns and 4 cm24 \mathrm{~cm}^2 face area is placed with its axis parallel to a magnetic field which decreases by 10−2 Wb10^{-2} \mathrm{~Wb} m−2\mathrm{m}^{-2} in 0.01 s0.01 \mathrm{~s}. The e.m.f. induced in the coil is:

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Answer: (A) 400mV400 \mathrm{mV}

Given: No. of turns N=1000N=1000
Face area, A=4 cm2=4×10−4 m2A=4 \mathrm{~cm}^2=4 \times 10^{-4} \mathrm{~m}^2
Change in magnetic field,
ΔB=10−2wbm−2\Delta \mathrm{B}=10^{-2} \mathrm{wbm}^{-2}
Time taken, t=0.01 s=10−2sect=0.01 \mathrm{~s}=10^{-2} \mathrm{sec}
Emf induced in the coil e=e= ?
Applying formula,
Induced emf, e=−dϕdte=\frac{-d \phi}{d t}
=N(ΔBΔt)Acos⁡θ=1000×10−2×4×10−410−2=400mV\begin{aligned} &=N\left(\frac{\Delta B}{\Delta t}\right) A \cos \theta \\ &=\frac{1000 \times 10^{-2} \times 4 \times 10^{-4}}{10^{-2}}=400 \mathrm{mV} \end{aligned}

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