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


- A$\mathrm{Bv} \tan \frac{\theta}{2}$
- Correct answerB$\mathrm{Bv}^2 \tan \frac{\theta}{2}$
- 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'.