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

Answer 1

Answer: (C)

$\int d\epsilon =\int B(\omega x)dx$
$\epsilon =B\omega \underset{0}{\overset{L}{\int }}xdx=\frac{B\omega L^2}{2}$