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Consider the following statement I found in a physics book :

"The net flux through the surface is proportional to the net number of lines leaving the surface, where the net number means the number of lines leaving the surface minus the number of lines entering the surface. If more lines are leaving than entering, the net flux is positive. If more lines are entering than leaving, the net flux is negative."

I don't understand how can an electric field line enter a closed surface and does not leave it... These lines are infinite right ? So if a line is entering then it must also leave the surface. Can someone illustrate me the situation they are talking about ?

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2 Answers 2

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A closed surface containing a charge will have flux lines that originate at the charge which pass through the surface. In fact the net flux through a closed surface is proportional to the net charge enclosed by that surface. This is Gauss's Law for Electric Fields (Usually listed as the first of Maxwell's Equation, which were given to us in their modern form by Heaviside).

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  • $\begingroup$ Yes thank you, I initially didn't think of the case where we have a charge inside the closed surface. $\endgroup$
    – Kilkik
    Commented Jun 11, 2021 at 23:50
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The point is that if you, for example, have a charge at the center of a sphere, all field lines go straight out from the charge (or straight in, depending on whether the charge is positive or negative) and terminate there. So charges are sources and drains for these field lines. If there are no charges inside a closed surface, indeed all field lines entering it must also leave it, which is Gauss's law.

If we talk about general surfaces, not only closed ones, you immediately see that this is in general not true. Field lines can go through the surface one way and curve around past the edge of the surface, so they need not go back through that surface.

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  • $\begingroup$ Yes thank you, I initially didn't think of the case where we have a charge inside the closed surface. $\endgroup$
    – Kilkik
    Commented Jun 11, 2021 at 23:50

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