Question

A metal rod of resistance $20\Omega$ is fixed along a diameter of a conducting ring of radius 0.1 m and 1 on x – y plane. There is an magnetic field $\overrightarrow{B}=50T\hat{k}$. The ring rotates with an angularvelocity $\omega =20rad{s}^{-1}$ about its axis. An external resistance of $10\Omega$ is connected across the centre of the rod and rim. The current through external resistance is

• A. $=\frac{1}{4}A$
• B. $=\frac{1}{2}A$
• C. $=\frac{1}{3}A$
• D. $Zero$

Answer 1

The correct option is C $=\frac{1}{3}A$

$i=2\left[\frac{1}{2}\frac{B{r}^{2}w}{R}\right]$
$=\frac{50\times {10}^{-2}\times 20}{10+20}=\frac{{10}^3\times {10}^{-2}}{30}$
$=\frac{1}{3}A$