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 $\overrightarrow{B}$ $=(50T)\hat{k}$ . The ring rotates with an angular velocity $\omega =20rad{s}^{-1}$ about its axis. An external resistance of 10 $\Omega$ is connected across the centre of the ring and rim. The current through external resistance is

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

Answer 1

Answer: (B)

Here, resistance of rod $=2\Omega ,r=0.1m,B=50T,alongz-axis\omega =20rad{s}^{-1}.$
Potential difference between centre of the ring and the rim is
$V=\frac{1}{2}B\omega r^2=\frac{1}{2}\times 50\times 20\times {\left(0.1\right)}^2=5$ V
Current through external resistance,
$i=\frac{E}{R+r}=\frac{5}{10+5}=\frac{1}{3}$ A