Question

A metallic rod of length ' $L$ ' is rotated with an angular speed of ' $\omega$ ' normal to a uniform magnetic field ' $B$ ' about an axis passing through one end of rod as shown in figure. The induced emf will be :

• A. $ \frac{1}{2} B ^2 L ^2 \omega $
• B. $ \frac{1}{4} BL ^2 \omega$
• C. $\frac{1}{2} BL ^2 \omega $
• D. $ \frac{1}{4} B ^2 L \omega$

Answer 1

Answer: (C)

$ \int d \varepsilon=\int B(\omega x) d x $
$ \varepsilon=B \omega \int\limits_0^L x d x=\frac{B \omega L^2}{2}$