Question

Consider the situation shown in figure. The wire PQ has a negligible resistance and is made to slide on the three rails with a constant speed of 5 cm s−1. Find the current in the 10 Ω resistor when the switch S is thrown to (a) the middle rail (b) the bottom rail.
Figure

Answer 1

Current in Bottom rail is 0.2 mA

Explanation:

B = 1T, V =$\frac {5}{10}$or $2^-^1$, R = 10$\Omega$

(a) When the switch is thrown to the middle rail E = Bvℓ  

= $1 \times 5 \times 10^-^2 \times 2 \times 10^-^2$

= $10^-^3$

Current in the 10 no.s resistors = $\frac {E}{R}$

= $\frac {10^-^3}{10}$

= $10^-^4$ = 0.1 mA

(b) The switch is thrown to the lower rail  

E = Bvℓ

= $1 \times 5 \times 10^-^2 \times 2 \times 10^-^2$

= $20 \times 10^-^4$

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

= $2 \times 10^-^4$

= 0.2 mA