Question

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

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

Answer 1

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

The potential difference is $V=\frac{1Bw{r}^2}{2}=\frac{1\ast 20\ast 50(0.1{)}^2}{2}=5V$

The equivalent circuit is

$i=\frac{V}{R_1+R_2}=\frac{5}{10+5}=\frac{1}{3}A$