Given below are two statements:
Statement I: In Gauss’s law, the charge \(q\) is the total charge enclosed by the surface, wherever the charges are placed inside it.
Statement II: If the net electric flux through a closed surface is zero, the electric field must be zero at every point on that surface.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is correct but Statement II is incorrect
Gauss’s law says that the total flux through a closed surface equals \( q/\varepsilon_0 \), where \( q \) is the total charge enclosed by the surface.
Statement I In Gauss’s law, the charge \(q\) is the total charge enclosed by the surface, wherever the charges are placed inside it. — True. Only the total enclosed charge enters the law. Moving a charge to another place inside the surface does not change the total flux.
Statement II If the net electric flux through a closed surface is zero, the electric field must be zero at every point on that surface. — False. Zero net flux only tells us that the net charge inside is zero. Take a closed cylinder in a uniform field, with its axis along the field. The flux is \( -ES \) through one end and \( +ES \) through the other, so the total is zero. Yet the field is not zero anywhere on the surface.
NCERT (2026-27):
Gauss’s Law – “(ii) The term q on the right side of Gauss’s law, … includes the sum of all charges enclosed by the surface. The charges may be located anywhere inside the surface.”
Gauss’s Law – “Here the electric field is uniform and we are considering a closed cylindrical surface, with its axis parallel to the uniform field E. … Thus, the total flux is zero, as expected by Gauss’s law. …”