JEE Advanced 2017 · Paper 1 · Physics Q5

← JEE Advanced 2017 · Paper 1

PhysicsMultiple correct+4 / -2Question 5 of 54

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ 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 $\vec{B}$ points into the plane of the paper. At $t = 0$ , the loop starts rotating about the common diameter as axis with a constant angular velocity $\omega$ in the magnetic field. Which of the following options is/are correct?

A figure-of-eight wire loop in the plane of the paper: an upper circle of area A and a lower circle of area 2A, crossing (insulated) at the joint. A uniform field B points into the paper (crosses). The loop rotates with angular velocity ω about the vertical dashed line through both centres (the common diameter).

The emf induced in the loop is proportional to the sum of the areas of the two loops

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

The net emf induced due to both the loops is proportional to

\cos\omega t

The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper

Answer and worked solution

Official answer: B, D

Twisted loop. Twisting a loop into a figure of eight makes the current circulate in opposite senses in the two lobes. Their emfs therefore subtract. The effective area is
$2A-A=A.$

(A) The emf is proportional to the difference of the areas, not the sum. False.
(B) The net amplitude equals that of the smaller loop alone. True.
(C) $\Phi=BA\cos\omega t$ gives $\varepsilon=BA\omega\sin\omega t$ , not $\cos\omega t$ . False.
(D) $|d\Phi/dt|$ is largest when $\Phi=0$ , i.e. when the loops' plane is perpendicular to the paper (parallel to $\vec B$ ). True.

(B), (D)

Topics:Faraday's and Lenz's laws

← Previous question Next question →

JEE Advanced 2017 · Paper 1, Physics question 5