Question

A parallel plate capacitor (of capacitance C) with circular plates of radius $r_0$ located at positions $\pm \alpha$, is connected in series with a resistor $R$ and is charged by a battery of voltage $V$. Consider a circular loop $L$ of radius $\frac{r_0}{2}$ parallel to the capacitor plates is located at the center. Which of the following statements is correct?

• A. The charge on the capacitor at time t is q(t) = CR $(1 - e^{-t/(CV)})$
• B. The charge on the capacitor at time t is q(t) = CV$(1 - e^{-t/(CV)})$
• C. The flux through the loop L is independent of the area enclosed by it
• D. The magnetic field is directed orthogonal to the loop L
• E. The magnetic field is directed along the loop L

Answer 1

Answer: (E)

A parallel plate capacitor of plate radius $r_{0}$ located at position $\pm a$ is shown in figure below

As we know the charge on capacitor at time $t$
$q(t)=C V\left(1-e^{t / R C}\right)$
Flux through the circular loop $L$
$\phi =E A $
$=\frac{V'}{2 \alpha}\left(\pi \frac{r_{0}^{2}}{4}\right)=\frac{\pi}{8} \frac{r_{0}^{2} V'}{\alpha}$
So, the flux depend the area of circular loop. Both $B$ and E are in same direction, where magnetic field is directed along the loop $L$.