A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant…

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7 \times 10^8 \mathrm{~V} / \mathrm{s}$ then the integer value of the distance between the parallel plates is $\left(\right.$ Take, $\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)$ ________ $\mu \mathrm{m}$.

Solution

$\begin{aligned}
& Q=c V \\ & V=\frac{Q}{c}=\frac{i t}{\left(\frac{\varepsilon_0 A}{d}\right)} \\ & d=\frac{\varepsilon_0 \pi r^2}{i}\left(\frac{v}{t}\right)
\end{aligned}$
Putting values
$\begin{aligned}
d & =\frac{9 \times 10^{-12} \times \frac{22}{7} \times(0.1)^2}{0.15} \times\left(7 \times 10^8\right) \\ & =1320 \mu \mathrm{~m}
\end{aligned}$

Asked in: JEE Main 2025 (29 Jan Shift 2)

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