Verified Solution • 2025–26 Session moderate

QJEEAdv16Ph201e: JEE Advanced 2016 Physics - Class 12 JEEAdv16Ph201e Solution: A conducting loop in the shape of a right angled isosceles…

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90 ∘^\circ 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 As −- 1. Which of the following statement(s) is (are) true?

JEE Advanced 2016 Paper 1 Offline Physics - Electromagnetic Induction Question 11 English

Multiple Choice Options

  • A There is a repulsive force between the wire and the loop.
  • B If the loop is rotated at a constant angular speed about the wire, an additional emf of (μ0π)\left( {{{{\mu _0}} \over \pi }} \right) volt is induced in the wire
  • C The magnitude of induced emf in the wire is (μ0π)\left( {{{{\mu _0}} \over \pi }} \right) volt
  • D The induced current in the wire is in opposite direction to the current along the hypotenuse.

Step-by-Step Verified Solution

The flux passing through the triangular wire if ' ii ' current flows through the infinitely long conducting wire.

JEE Advanced 2016 Paper 1 Offline Physics - Electromagnetic Induction Question 11 English Explanation 1
dIdtamp;=10As−1ϕamp;=∫00.1μ0i2πx×2xdxϕamp;=μ0i10π=Mi\begin{aligned}\frac{d \mathrm{I}}{d t} & =10 \mathrm{As}^{-1} \\\\\phi & =\int_0^{0.1} \frac{\mu_0 i}{2 \pi x} \times 2 x d x \\\\\phi & =\frac{\mu_0 i}{10 \pi}=\mathrm{M} i\end{aligned}

∴M=μ010π\therefore \mathrm{M}=\frac{\mu_0}{10 \pi}

 Induced emf in the wire =Mdidt=μ010π×10=μ0π\text { Induced emf in the wire }=\frac{\mathrm{M} d i}{d t}=\frac{\mu_0}{10 \pi} \times 10=\frac{\mu_0}{\pi}

According to Lenz's law, the induced current opposes the flux change that creates it. Since the flux is increasing, the induced emf opposes the existing magnetic field and the current flows from left to right in the straight wire, that is, along the hypotenuse current. That is, there is a repulsive force between the wire and the loop.

JEE Advanced 2016 Paper 1 Offline Physics - Electromagnetic Induction Question 11 English Explanation 2
Also, if the loop is rotated about the wire, there is no change in the flux through the wire, so no extra induced emf is generated in the wire.

Related Learning Resources & Exam Preparation

JEE Advanced PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring