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 $2\text{T}$ as shown in the figure. The induced emf between the point $\text{A}$ & $\text{B}$ of the 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 $0.051\text{V}$

Emf induced in a rotating conductor of length $l$, with angular velocity $\omega$ in magnetic field $B$ is

$E=\frac{B\omega l^2}{2}$

$\therefore E_B=\frac{B\omega l{{}_B}^2}{2}$, and

$E_A=\frac{B\omega l{{}_A}^2}{2}$

$\therefore E_A-E_B=\frac{B\omega }{2}(l{{}_A}^2-l{{}_B}^2)$

$=\frac{2\times 10}{2}({0.1}^2-{0.07}^2)$

$\Rightarrow E_A-E_B=10(0.01-0.0049)$

$\therefore E_A-E_B=0.051\text{V}$

Hence, option $\left(C\right)$ is correct.