Question

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_o e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

• A. $B_o \omega \left[ \frac{1}{\lambda^2} - e^{-\lambda L} \left( \frac{1}{\lambda^2} + \frac{L}{\lambda} \right) \right]$
• B. $B_o \omega \left[ \frac{1}{\lambda^2} + e^{-\lambda L} \left( \frac{1}{\lambda^2} + \frac{L}{\lambda} \right) \right]$
• C. $B_o \omega \left[ \frac{4}{\lambda^2} - e^{-2\lambda L} \left( \frac{1}{\lambda^2} + \frac{2L}{\lambda} \right) \right]$
• D. $B_o \omega \left[ \frac{3}{\lambda^2} - e^{-3\lambda L} \left( \frac{3}{\lambda^2} + \frac{L}{\lambda} \right) \right]$

Answer 1

The Correct Option is A