Physics Question from JEE Main 2025 · 29 January, Shift 2

A parallel plate capacitor consisting of two circular plates of radius $10 \, \text{cm}$ is being charged by a constant current of $0.15 \, \text{A}$. If the rate of change of potential difference between the plates is $7 \times 10^{8} \, \text{V/s}$, then the integer value of the distance between the parallel plates is _______ $\mu\text{m}$.

$\left(\text{Take } \varepsilon_0 = 9 \times 10^{-12} \, \frac{\text{F}}{\text{m}}, \; \pi = \frac{22}{7}\right)$