Electromagnetic Induction

JEE Main level, single correct, medium

36 of 153

Question 36 of 153

A planar loop of wire rotates in a uniform magnetic field. Initially, at t=0t=0 , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10s10s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

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Answer: (B) 2.5s2.5s and 5.0s5.0s

Φ=B⃗⋅A⃗=BAcos⁡θ=BAcos⁡(ωt)\Phi =\vec{B}\cdot \vec{A}=BA\cos \theta =BA\cos \left(\omega t\right)
e=∣dϕdt∣=BAωsin⁡(ωt)e=\left|\dfrac{d\phi }{dt}\right|=BA\omega \sin \left(\omega t\right)

When ωt=π2\omega t=\dfrac{\pi }{2}
∵ϕ∵\phi will be minimum.
∴e∴e will be maximum
t=π2π5=2.5st=\dfrac{\dfrac{\pi }{2}}{\dfrac{\pi }{5}}=2.5s
When ωt=π\omega t=\pi
∵ϕ∵\phi will be maximum.
∴e∴e will be minimum
t=ππ/5=5st=\dfrac{\pi }{\pi /5}=5s

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