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 anti-clockwise.
(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 of the following options are correct?

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Statements (i) and (iii) are correct.

Statements (ii) and (iv) are correct.

Statements (i), (iii) and (iv) are correct.

None of these

answer is C.

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Detailed Solution

$V_{C} = B v l$

$\begin{array}{rcl} ∴ q & = & C V_{C} = B v l C = constant \\ ∴ I_{C} & = & \frac{d q}{d t} = 0 \\ U_{C} & = & \frac{1}{2} C V^{2} = \frac{1}{2} C B^{2} L^{2} v^{2} \end{array}$

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