Question

A metal rod of resistance $20 \, \Omega $ is fixed along a diameter of a conducting ring of radius $0.1 \, m$ and lies on $x-y$ plane. There is a magnetic field $\overset{ \rightarrow }{B}$ $=\left(\right.50 \, T\left.\right) \, \hat{k}$ . The ring rotates with an angular velocity $\omega =20 \, rad \, 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 $=2\Omega , \, r=0.1 \, m, \, B=50 \, T, \, along \, z-axis \, \omega =20 \, rad \, s^{- 1}.$
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