Q72 / 75 · JEE Main 2025 (29 Jan Shift 2) · Physics
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, $\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)$ ________ $\mu \mathrm{m}$.
Correct answer: 1320
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
$\begin{aligned}
d & =\frac{9 \times 10^{-12} \times \frac{22}{7} \times(0.1)^2}{0.15} \times\left(7 \times 10^8\right) \\
& =1320 \mu \mathrm{~m}
\end{aligned}$
Hence, the correct answer is 1320.