Why does a Charge Outside a Surface Produce No Net Flux?

In summary, a closed surface that does not contain any net charge will have a net flux of zero. This is because any incoming field lines from an external field will also have an equal number of outgoing field lines. This concept can be illustrated by drawing a source with field lines coming out of it and a closed shape that does not include the source. When counting the field lines going in and out, the net flux will always be zero.
  • #1
patrickbotros
34
1
My textbook says "the net flux is zero through a closed surface that does not contain any net charge," and justifies it by saying that everything flowing in has an equal thing flowing out. This makes ABSOLUTELY NO sense to me.
 
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  • #2
Nonetheless it is true.

If you saw it work in 2-D would you believe it in 3-D? Draw a source with field lines coming out of it. You can draw the field lines any way you want, provided that they do not cross. Now, draw a closed shape that does not include the source anywhere on the paper. Any closed shape. Count the lines going in and count the lines going out.
 
  • #3
In a surface that contains a source, for example a positive charged particle, the flux is determined by only outcoming field lines from it, while in a surface that doesn't contain any source, the field lines passing through it, generated by an external field , enter but also go out, and so the net flux is zero.
 

FAQ: Why does a Charge Outside a Surface Produce No Net Flux?

Why does a charge outside a surface produce no net flux?

According to Gauss's Law, the net electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. Since the charge outside the surface is not enclosed by the surface, it does not contribute to the net electric flux.

Is it possible for a charge outside a surface to contribute to the net flux?

No, according to Gauss's Law, only the charge enclosed by a closed surface can contribute to the net electric flux through that surface. Any charge outside the surface does not affect the net flux.

How does the distance of the charge from the surface affect the net flux?

The distance of the charge from the surface does not affect the net flux. As long as the charge is outside the closed surface, it will not contribute to the net flux according to Gauss's Law.

Can a charge inside the surface produce net flux?

Yes, a charge inside the surface can produce net flux through the surface. This is because the charge is enclosed by the surface and therefore contributes to the net flux according to Gauss's Law.

Does the size of the surface affect the net flux produced by a charge outside?

No, the size of the surface does not affect the net flux produced by a charge outside. The net flux is only affected by the charge enclosed by the surface, not the size of the surface itself.

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