Question

There is a pair of fixed, parallel rails of negligible resistance in a horizontal plane, at a distance of $L=10 \, cm$ . The rails are connected, at one of their ends to an ideal battery of EMF $0.5 \, V$ , as shown in the figure. The system is placed in a vertically downward and perpendicular magnetic field of magnetic induction $B=1 \, T$ . A metal rod of resistance $R=10 \, \Omega$ is placed perpendicularly on the rails. The rod and rails are frictionless. The magnitude of force, which is to be exerted on the rod in order to move it with a constant speed of $1 \, ms^{- 1}$ in the direction shown, is

• A. $2\times 10^{- 3} \, N$
• B. $4\times 10^{- 3} \, N$
• C. $8\times 10^{- 3} \, N$
• D. $5\times 10^{- 3} \, N$

Answer 1

Answer: (B)

$\epsilon _{i n}=B\cdot L\cdot V=1\times 10\times 10^{- 2}\times 1$
$\epsilon _{i n}=0.1 \, V$

$I=\frac{0.5 - 0.1}{10}=0.04$
$\left|\overset{ \rightarrow }{F}\right|=1\times 0.04\times 10^{- 2}\times 10$
$=0.4\times 10^{- 2}$
$\left|\right.\overset{ \rightarrow }{F}\left|\right. \, =4\times 10^{- 3} \, N$