Electromagnetic Induction

JEE Main level, numerical answer, medium

34 of 153

Question 34 of 153

A circular coil of radius 10cm10cm is placed in a uniform magnetic field of 3.0×10−5T3.0\times {10}^{-5}T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2s0.2s. The maximum value of EMF induced (in μV\mu V) in the coil will be close to the integer....

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Answer: 15

Flux as a function of time ϕ=B⃗⋅A⃗=ABcos⁡(ωt)\phi =\vec{B}\cdot \vec{A}=AB\cos (\omega t)
Emf induced,
e=−dϕdt=ABωsin⁡(ωt)e=\dfrac{-d\phi }{dt}=AB\omega \sin (\omega t)
Max. value of Emf =ABω=AB\omega
=πR2Bω=\pi {R}^{2}B\omega
=3.14×0.1×0.1×3×10−5×π0.2=15=3.14\times 0.1\times 0.1\times 3\times {10}^{-5}\times \dfrac{\pi }{0.2}=15

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