If the flux of the electric field through a closed surface is zero,

Options

A. electric field intensity at all points on the Gaussian surface may be non-zero.
B. electric field intensity at all points on the Gaussian surface may be zero
C. electric field intensity at some points on the Gaussian surface must be zero.
D. electric field intensity at some points on the Gaussian surface may be non-zero.

Answer

A, B, D

Explanation

This question talks about the possibilities behind zero electric flux linked with some Gaussian surfaces.
Electric field intensity everywhere on a Gaussian surface may be non-zero because a reason behind zero flux may be `90^@` angle between electric field and surface normal. Also, sometimes positive electric flux over some portion of Gaussian surface is cancelled due to equal and negative electric flux linked with some other portion of the same Gaussian surface. So, option (a) is correct. In a situation, if the electric field intensity everywhere on the Gaussian surface is zero then the net electric flux associated with the Gaussian surface must become zero. Thus, ption (b) is correct.
It is not necessary that electric field intensity in some portion of Gaussian surface must be zero in order for the total flux to become zero. Option (c) is not correct. But the electric field intensity may be zero at some points and in the same way it may be non-zero also for some points, hence option (d) is correct.