Physics Question 5 – NEET-UG 2023

The problem states that ${\oint }_S\overrightarrow{E}\cdot d\overrightarrow{S}=0$. According to Gauss's Law, this implies that the net charge enclosed by the surface, $Q_{enc}$, must be zero.

If the net flux is zero, it means that the number of electric field lines entering the surface must be equal to the number of field lines leaving it, as there is no net source or sink of flux within the surface. This is consistent with $Q_{enc}=0$. Therefore, option (1) is correct. Option (2) is incorrect because the electric field magnitude on the surface is not necessarily constant. Charges outside the surface can create a non-uniform field on the surface, even if $Q_{enc}=0$. Option (3) is incorrect because if $Q_{enc}=0$, it means the *net* charge inside is zero. It does not mean "all charges" (if any exist) must be inside, nor does it preclude charges existing outside the surface. Option (4) is incorrect because the electric field inside the surface is not necessarily uniform. For example, an electric dipole inside the surface results in $Q_{enc}=0$ but a non-uniform field.