Question

Consider the situation shown in figure (38-E18). The wire PQ has a negligible resistance and is made to slide on the three rails with a constant speed of $5cm{s}^{-1}$. Find the current in the $10\Omega$ resistor when the switch S is thrown to (a) the middle rail (b) the bottom rail.

Answer 1

Here B=1 T,

$v=5\times {10}^{-2}m/sR=10\Omega$

(a)When the switch is thrown to the middle rail

E =Bvl

$=1\times 5\times {10}^{-2}\times 2\times {10}^{-2}V$

$=10\times {10}^{-4}={10}^{-3}V$

Curret in the 10 $\Omega$ resistor

$=\frac{E}{R}$

$=\frac{{10}^{-3}}{10}={10}^{-4}=0.1mA.$

(b)The switch is thrown to the lower rail

E =Bvl

$=1\times 5\times {10}^{-2}\times 4\times {10}^{-2}$

$=20\times {10}^{-4}V$

Current $=\frac{20\times {10}^{-4}}{10}$

$=2\times {10}^{-4}V=0.2mA.$