Question

A conducting rod is moving with a constant velocity $v$ over the parallel conducting rails which are connected at the ends through a resistor $R$ and capacitor $C$ as shown in the figure. Magnetic field $B$ is into the plane. Consider the following statements:
(i) Current in loop $AEFBA$ is anticlockwise.
(ii) Current in loop $AEFBA$ is clockwise.
(iii) Current through the capacitor is zero.
(iv) Energy stored in the capacitor is $\frac{1}{2}C{B}^2{L}^2{V}^2$
Which if the following options is correct?

• A. Statements (i) and (iii) are correct
• B. Statements (ii) and (iv) are correct
• C. Statements (i), (iii) and (iv) are correct
• D. None of these

Answer 1

The correct option is C Statements (i), (iii) and (iv) are correct

$V_C=Bvl$

$\therefore$ $q=C{V}_C=BvlC=$ constant

$\therefore$ $I_C=\frac{dq}{dt}=0$

$U_C=\frac{1}{2}C{V}^2$

$=\frac{1}{2}C{B}^2{L}^{2}v$