Electromagnetic Induction — JEE Advanced · 2016 · 22 May 2016 · Paper 1 Question with Solution

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s

^{- 1}

. Which of the following statement(s) is(are) true?
(A) The magnitude of induced emf in the wire is

(\frac{μ _{0}}{π})

volt
(B) If the loop is rotated at a constant angular speed about the wire, an additional emf of

(\frac{μ _{0}}{π})

volt is induced in the wire
(C) The induced current in the wire is in opposite direction to the current along the hypotenuse
(D) There is a repulsive force between the wire and the loop

(A)The magnitude of induced emf in the wire is $(\frac{μ _{0}}{π})$ volt✓ Correct
(B)If the loop is rotated at a constant angular speed about the wire, an additional emf of $(\frac{μ _{0}}{π})$ volt is induced in the wire
(C)The induced current in the wire is in opposite direction to the current along the hypotenuse
(D)There is a repulsive force between the wire and the loop✓ Correct

Answer: (A), (D)

Solution

The magnetic flux through the wire due to the loop's current

I

is:

ϕ = \int_{0}^{h} \frac{μ _{0} I}{2 π r} \cdot 2 r d r = \frac{μ _{0} I h}{π}

The mutual inductance is

M = \frac{μ _{0} h}{π} = \frac{μ _{0} \times 0.1}{π}

.

The induced emf in the wire is:

ε = M \frac{d I}{d t} = \frac{μ _{0} \times 0.1}{π} \times 10 = \frac{μ _{0}}{π}

volt. (A) is correct.

Rotation at constant angular speed does not change the flux through the wire (symmetry), so no additional emf is induced. (B) is incorrect.

By Lenz's law, the induced current in the wire opposes the change, creating a repulsive force. The current direction is such that it opposes the increasing flux. (C) is incorrect in its specific claim, but (D) is correct.

JEE Advanced · 2016 · 22 May 2016 · Paper 1 · One or more correct options

JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Electromagnetic Induction

Solution

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