Electromagnetic Induction

JEE Main level, single correct, medium

56 of 153

Question 56 of 153

A coil of cross-sectional area AA having nn turns is placed in a uniform magnetic field BB. When it is rotated with an angular velocity ω,\omega , the maximum e.m.f. induced in the coil will be:

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Answer: (C) nBAωnBA\omega

Magnetic flux through a coil of area AA of nn turns at an angle θ\theta to the magnetic field of magnitude BB is, ϕ=nBAcosθ=nBAcosωt\phi =nBAcos\theta =nBAcos\omega t. The induced emf,

ϵ=∣dϕdt∣=nBAωsin⁡⁡ωt\epsilon =\left|\dfrac{d\phi }{dt}\right|=nBA\omega \sin ⁡\omega t. Since, the maximum value of the sine function is 11,

ϵmax=nBAω{\epsilon }_{max}=nBA\omega

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