Question

Wire $PQ$ with negligible resistance slides on the three rails with $5\text{cm/s}$. Calculate the magnitude of currents in $10\Omega$ resistor when switch $S$ is connected to position $1$ and $2$ one after the other, respectively.

• A. $1\text{mA},2\text{mA}$
• B. $2\text{mA},1\text{mA}$
• C. $0.1\text{mA},0.2\text{mA}$
• D. $0.2\text{mA},0.1\text{mA}$

Answer 1

The correct option is C $0.1\text{mA},0.2\text{mA}$


For switch in position $1$:

Length of rod, $l_1=2\text{cm}=2\times {10}^{-2}\text{m}$

Velocity of rod, $v=5\text{cm/s}=5\times {10}^{-2}\text{m/s}$

$R=10\Omega$

$B=1\text{T}$

$\therefore$ Induced current,

$I_1=\frac{{ϵ}_1}{R}=\frac{Bv{l}_1}{R}=\frac{1\times 5\times {10}^{-2}\times 2\times {10}^{-2}}{10}$

$\Rightarrow I_1=0.1\text{mA}$

For switch in position $2$ :

Length of rod, $l_2=(2+2)\text{cm}=4\text{cm}$

$=4\times {10}^{-2}\text{m}$

$\therefore$ Induced current,

$I_2=\frac{{ϵ}_2}{R}=\frac{Bv{l}_2}{R}=\frac{1\times 5\times {10}^{-2}\times 4\times {10}^{-2}}{10}$

$\Rightarrow I_2=0.2\text{mA}$