Electric flux textbook discrepancy ?

[jaredvert]

Electric flux textbook discrepancy ??

my textbook says "q enclosed for the Guastian surface in a1 would be the positive charge enclosed by a1: the negative charge does contribute to the electric field at a1 but it is not enclosed by surface a1 and so is not included in q enclosed". ...…..;…. So I would be quicker to deduce that I made the error than my textbook but the I thought the net electric flux is defined by the flux entering or leaving that doesn't begin or end in the enclosed surface. Since the electric field stops in the surface doesn't that mean it now has that net flux ? Or does this just not contribute to gauss's law? If so please elucidate! I'm only in ap physics so don't go beyond mechanics and basic e and m since I just started! ThanksSent from my iPhone using Physics Forums

 

[Simon Bridge]

woah - big photo!
It shows an electric dipole with well separated charges.
The flux through surface A1 is positive while the flux through A2 is negative.
Both sets of charge contribute to the electric field everywhere, but the net flux through a surface is determined by the charge enclosed by the surface. The sign of the charge determines the direction.

You can actually see this in your diagrams - the flux is just the number of field lines through a surface.
The number of field lines starting or ending on a charge is a fixed number - determined by the amount of charge.

So if you have two equal and opposite charges, then they both have the same number of field lines attached to them - bring them close and all the field lines starting on the positive charge can end up on the negative charge and the total number of lines on each charge stays the same.

If you draw a surface around a volume with zero charge in it, but there are charges outside it, you'll see that all the field lines that enter the surface also leave it - so the net flux through the surface is zero.