JEE Main 2025 — Electrostatics Question with Solution

Given an electric flux $\varphi =-2\times 10^4{\text{Nm}}^2{\text{C}}^{-1}$ through a spherical Gaussian surface with a radius of 8.0 cm (r = 0.08 m), we are to find the value of the point charge $Q$. According to Gauss's Law:

$\varphi =\frac{Q}{{\epsilon }_0}$

Where ${\epsilon }_0=8.85\times 10^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$.

Rearranging the equation to solve for $Q$, we have:

$Q=\varphi {\epsilon }_0$

Substituting the given values:

$Q=-2\times 10^4\times 8.85\times 10^{-12}$

Calculating this yields:

$Q=-17.7\times 10^{-8}\text{C}$

Thus, the value of the point charge is $Q=-17.7\times 10^{-8}\text{C}$.