Understanding the Sign of Electric Flux on a Cylindrical Surface

Electric flux is a measure of the number of electric field lines passing through a given surface. According to Gauss’s Law, the electric flux through a closed surface is proportional to the net electric charge enclosed within that surface.

In this case, the red lines represent the electric field vectors on the surface of a cylinder. If these vectors are directed outward from the surface, they indicate that the electric field is emerging from the enclosed region. This typically means that there is a positive charge inside the cylinder, and hence the electric flux is positive.

Conversely, if the red electric field vectors were pointing inward toward the surface of the cylinder, it would suggest that the electric field lines are entering the surface. That would correspond to a negative electric flux, implying a net negative charge inside the cylinder.