Question

Two infinitely long conducting parallel rails are connected through a capacitor $C$ as shown in the figure. A conductor of length $l$ is moved with constant speed $V_0$. Which of the following graph truly depicts the variation of current through the conductor with time?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Emf induced across the conductor or capacitor is given by,

$E=|-\frac{d\varphi }{dt}|=Bl\frac{dx}{dt}$

$\therefore E=B{V}_{0}l$

The charge on the capacitor,

$q=CE=CB{V}_{0}l=\text{constant}$

Now, the induced current,

$I=\frac{dq}{dt}=\frac{d\left(CB{V}_{0}l\right)}{dt}=0$

So, no current will flow in the circuit.

The graph is plotted as shown below.


Hence, $\left(B\right)$ is the correct answer.