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JEE Main 20207 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2020 · 7 January · Evening Shift · Physics · Electromagnetic Induction

A planar loop of wire rotates in a uniform magnetic field....

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:

Options

  1. A2.5s2.5s and 7.5s7.5s
  2. B2.5s2.5s and 5.0s5.0s
  3. C5.0s5.0s and 7.5s7.5s
  4. D5.0s5.0s and 10.0s10 . 0s

Correct answer

B. 2.5s2.5s and 5.0s5.0s

Step-by-step solution

Φ=B→⋅A→=BAcosθ=BAcos(\omegat)Φ = \overset{\to}{B} \cdot \overset{\to}{A} = BAcos\theta = BAcos\left(\omegat\right)

e=∣dϕdt∣=BAωsin(\omegat)e = \left|\dfrac{dϕ}{dt}\right| = BA\omega sin\left(\omegat\right)


When \omegat=π2\omegat = \dfrac{\pi}{2}
∵ϕ∵ ϕ will be minimum.
∴e∴ e will be maximum
t=π2π5=2.5st = \dfrac{\dfrac{\pi}{2}}{\dfrac{\pi}{5}} = 2 . 5s

When \omegat=π\omegat = \pi
∵ϕ∵ ϕ will be maximum.
∴e∴ e will be minimum
t=ππ/5=5st = \dfrac{\pi}{\pi / 5} = 5s

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