It\'s being said \"A point charge located outside a closed surface. Because the

Question

It's being said "A point charge located outside a closed surface. Because the number of lines(electric fields vectors) entering the surface equals the number leaving the surface, the net electric flux through a closed surface that has no charge is zero." I understand this one. I came across a problem while solving exercises that is: "A particle with charge q is located a distance d from an infinite plane. Determine the electric flux through the plane due to the charged particle." I was amazed that the electric flux now has a formula of 1/2 * q * (Epsilon Zero)[According to their solution]. Shouldn't the number of lines(electric fields vectors)(that are emerging from my point charge) entering the surface equals the number leaving the surface? Please anyone's explanations are appreciated?

Explanation / Answer

As the plane is only a 2-D surface, there can only be a flux entering or leaving the plane,i.e when field lines pass one surface, the lines pass the opposite side simultaneously. In the case of the sphere, which is a closed surface,lines enter through a different surface and go through a different one

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