# Location of charge inside a gaussian surface

I'm aware that location of charge enclosed within gaussian surface doesn't affects the net flux through the closed surface . But I wanted to know wether location affects flux through particular face.

Consider the case of a cube if the charge is place at centre then flux through each face will be equal . But what happens when it is not at center?

Does the face nearer to charge has greater flux?

• The flux through each of the faces will depend on the position of the charge within your closed surface. Commented Apr 14, 2017 at 20:13

I pulled out my best drawing skills to make the following image that explains the situation (in 2D):

The red lines emitting from the charge represent electrical flux, counting the flux trough a surface becomes really easy, we just count the number of flux lines that pierce it.

We see two drawn squares (= cubes) one of them has flux of 7 blue "fluxlines" passing trough, the other has 9 blue and red passing trough. Such that indeed, the number of flux lines passing trough the surface of a square(=cube) depends on its positions relative to the charge.

However, you should notice that the total amount of fluxlines crossing the square does not depend on its position with respect to the charge as long as it is inside the square !

I hope that this helped you gain some intuition ? :)

In the limit of a charge that is very close to one of the faces of your cube, it's obvious to see there are far more lines going through one face than the other:

You can conclude that the charge distribution, in general, will affect the flux through a particular surface. Do you see it now?

If you consider the the total electric flux through a closed surface, it depends only on the total charge enclosed by the surface. The total flux is insensitive to the exact location of the charge within the surface. Now if you want to calculate the total flux through a part of the total surface, then it depends on the location of the charge in general. But one can think of particular case where it still might be insensitive to the location of the charge to some degree. For example if you consider an uniformly charged plane and a flux through a planer disc, the flux through the disc is independent of its distance from the plane provided you keep the orientation of the disc with respect to the surface fixed.