Question

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

Answer 1

Given length of the rod $l=10cm$; magnetic field $B=2T$ and angular speed $\omega =10rad/s$

Considering a elemental length dr at a distance x from end O.

Emf experienced by the elementary length of the conductor

$dϵ=BVdx$ here $v=\omega r$

Thus the above equation becomes

$dϵ=B\omega rdr$

Now potential difference between the points A and B is

$ϵ={\int }_{0.07}^{0.1}B\omega rdr$

$=B\omega {\frac{r^2}{2}}_{0.07}^{0.1}$

$2\times 10\times \frac{({0.1}^2-{0.07}^2)}{2}=0.051V$