Q142 / 155 · WBJEE 2024 · Physics

Two straignt conducting plates form an angle $\theta$ where their ends are joined. A conducting bar in contact with the plates and forming an isosceles triangle with them starts at the vertex at time $t=0$ and moves with constant velocity $\vec{v}$ to the right as shown in figure. A magnetic field $\vec{B}$ points out of the page. The magnitude of emf induced at $t=1$ second will be Figure

  • A
    $\mathrm{Bv} \tan \frac{\theta}{2}$
  • Correct answer
    B
    $\mathrm{Bv}^2 \tan \frac{\theta}{2}$
  • C
    $2 \mathrm{Bv}^2 \tan \frac{\theta}{2}$
  • D
    $2 \mathrm{Bv}^2 \sin \frac{\theta}{2}$

Solution

Hint : $\ell=2 \mathrm{vt} \tan \frac{\theta}{2}$ $$ \varepsilon=\mathrm{B} \ell \mathrm{v}=2 \mathrm{Bv} \mathrm{v}^2 \tan \frac{\theta}{2} $$

Hence, the correct answer is option: 'B'.

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