Q 12-01-041JEE MainJEE Main 2025 (29 Jan, Shift 2)Easy
A point charge causes an electric flux of $-2\times10^4\ \text{N m}^2\text{C}^{-1}$ to pass through a spherical Gaussian surface of $8.0\ \text{cm}$ radius, centred on the charge. The value of the point charge is (Given $\epsilon_0 = 8.85\times10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$)
Answer: (D) $-17.7\times10^{-8}\ \text{C}$
Gauss's law: $\phi = \dfrac{q}{\epsilon_0}$, independent of the sphere's radius.
$$q = \epsilon_0\phi = 8.85\times10^{-12}\times(-2\times10^4) = -17.7\times10^{-8}\ \text{C}$$
Solution by Sreeraj P, M.Sc Physics