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

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SUMMARY

The discussion clarifies that the net electric flux through a closed surface is zero if it does not enclose any net charge, as stated by Gauss's Law. This principle is illustrated by considering field lines from a charge source; when a closed surface does not contain the charge, the number of field lines entering the surface equals the number of lines exiting it. Therefore, the net flux remains zero. This concept is fundamental in understanding electric fields and their interactions with surfaces.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric field lines and their properties
  • Basic knowledge of closed surfaces in three-dimensional space
  • Concept of net charge and its implications in physics
NEXT STEPS
  • Study Gauss's Law and its applications in electrostatics
  • Explore the concept of electric field lines in detail
  • Investigate the properties of closed surfaces in three-dimensional geometry
  • Learn about the implications of net charge in various physical scenarios
USEFUL FOR

Students of physics, educators teaching electrostatics, and anyone interested in the principles of electric fields and their mathematical descriptions.

patrickbotros
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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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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.
 
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.
 

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