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JEE Advanced 2024Paper 2
Exam
JEE Advanced
Year
2024
Paper
Paper 2
Subject
Physics
Chapter
Electromagnetic Induction

JEE Advanced 2024 · Paper 2 · Physics · Electromagnetic Induction

A region in the form of an equilateral triangle (in x-y plane) of...

A region in the form of an equilateral triangle (in x−yx-y plane) of height LL has a uniform magnetic field B⃗\vec{B} pointing in the +z+z-direction. A conducting loop PQR\mathrm{PQR}, in the form of an equilateral triangle of the same height LL, is placed in the x−yx-y plane with its vertex P\mathrm{P} at x=0x=0 in the orientation shown in the figure. At t=0t=0, the loop starts entering the region of the magnetic field with a uniform velocity v⃗\vec{v} along the +x+x-direction. The plane of the loop and its orientation remain unchanged throughout its motion. A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field B pointing in Which of the following graph best depicts the variation of the induced emf (E)(E) in the loop as a function of the distance (x)(x) starting from x=0x=0 ?

Options

  1. AEight persons from different banks viz., Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Oriental
  2. BEight persons from different banks viz., Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Oriental
  3. CEight persons from different banks viz., Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Oriental
  4. DEight persons from different banks viz., Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Oriental

Correct answer

A. Eight persons from different banks viz., Bank of India, Punjab National Bank, Canara Bank, Bank of Baroda, Oriental

Step-by-step solution

For, 0 to L\mathrm{L} A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field B pointing in ε=Bℓeff \varepsilon=\mathrm{B} \ell_{\text{eff }}\mathrm{v}=\mathrm{B}×x3v\times \frac{\mathrm{x}}{\sqrt{3}} \mathrm{v} For, L\mathrm{L} to 2 L2 \mathrm{~L}A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field B pointing in
∣emf∣=B(L3−x03)v−B2x03v=BvL3−3Bvx0=Bv⁡[L3−3(x−L)]=Bv3[L−3x+3 L]=Bv3[4L−3x] at x=4L3emf=0\begin{aligned} & |e m f|=B\left(\frac{L}{\sqrt{3}}-\frac{x_0}{\sqrt{3}}\right) v-B \frac{2 x_0}{\sqrt{3}} v \\ & =\frac{B v L}{\sqrt{3}}-\sqrt{3} \mathrm{Bvx}_0 \\ & =\operatorname{Bv}\left[\frac{L}{\sqrt{3}}-\sqrt{3}(x-L)\right] \\ & =\frac{B v}{\sqrt{3}}[L-3 \mathrm{x}+3 \mathrm{~L}] \\ & =\frac{B v}{\sqrt{3}}[4 L-3 \mathrm{x}] \\ & \text{ at } x=\frac{4 L}{3} \\ & e m f=0 \\ & \end{aligned}
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