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JEE Advanced 2017Paper 1
Exam
JEE Advanced
Year
2017
Paper
Paper 1
Subject
Physics
Chapter
Electromagnetic Induction

JEE Advanced 2017 · Paper 1 · Physics · Electromagnetic Induction

A circular insulated copper wire loop is twisted to form two loops...

 A circular insulated copper wire loop is twisted to form two loops of area AA and 2A2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field B→\overset{\to}{B} points into the plane of the paper. At t=0t = 0 , the loop starts rotating about the common diameter as axis with a constant angular velocity in the magnetic field. Which of the following options is/are correct?
A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the

Options

  1. AThe net emf induced due to both the loops is proportional to cos\omegatcos \omegat
  2. BThe amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of the maximum emf induced in the smaller loop alone
  3. CThe rate of change of flux is maximum when plane of loop is perpendicular to the plane of paper
  4. DThe emf induced in the loop is proportional to sum of areas of two loops

Correct answer

B. The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of the maximum emf induced in the smaller loop alone

Step-by-step solution

A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the

When a conducting loop rotating in a magnetic field BBhas an angular velocity ω\omega, the flux through the loop of area AA at an angle θ=\omegat\theta = \omegat, 

ϕ=∣B∣∣A∣cosθϕ = \left|B\right|\left|A\right|cos \theta

=BAcos(\omegat)= BAcos \left(\omegat\right)

The induced emf,

ε=−dϕdt=BAωsin(\omegat)ε = - \dfrac{dϕ}{dt} = BA\omega sin \left(\omegat\right)

So, εanddϕdt∝sin⁡(\omegat)εand\dfrac{dϕ}{dt} ∝ \sin \left(\omegat\right)

So, the emf is maximum when, \omegat=θ=π2.\omegat = \theta = \dfrac{\pi}{2} .

Since the emf in the smaller loop will act opposite to that of the larger loop,

εNet=ε2A−εA=B(2A)ωsin\omegat−B(A)ωsin(\omegat){ε}_{Net} = {ε}_{2A} - {ε}_{A} = B\left(2A\right)\omega sin \omegat - B\left(A\right)\omega sin \left(\omegat\right)

=B(2A−A)ωsin\omegat=BAωsin\omegat= B\left(2A - A\right)\omega sin \omegat = BA\omega sin \omegat

So, the amplitude of the maximum net emf is equal to BABA which is same as that in the smaller loop.

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