Question

A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with constant angular velocity $10\text{rad/s}$ about point $O$, in constant magnetic field of $2T$ as shown in the figure. The induced emf between the point $A$ and $B$ of rod will be:

• A. $0.029\text{V}$
• B. $0.1\text{V}$
• C. $0.051\text{V}$
• D. $0.064\text{V}$

Answer 1

The correct option is C $0.051\text{V}$

We know that in pure rotational motion
$V=\omega r$
$\therefore e_{AB}=\underset{0.07}{\overset{0.1}{\int }}\left(B\right)\left(\omega r\right)dr=\underset{0.07}{\overset{0.1}{\int }}\left(2\right)\left(10r\right)dr=0.051\text{V}$