Net flux through a cylinder from a point charge

[henry3369]

Homework Statement

My book demonstrates how a uniform electric field through a box generates a net flux of zero. I was wondering if the same would happen from a point charge outside of the cylinder on one end instead of a uniform electric field.

Homework Equations

Flux = E⋅A

The Attempt at a Solution

My book says that charges outside of the surface do not give a net electric flux through the surface. So does that mean if a positive point charge is at one end of the cylinder, all the flux cancels out?

The flux through the nearest face would be negative because E and A are in opposite directions and the flux on the other end would be positive BUT smaller in magnitude because E is smaller (because the distance would increase) while A stays the same. And the flux around the surface would be positive.
So is:
Φ_{nearest face} = Φ_{further face} + Φ_{around the cylinder} ?

 

[Doc Al]

Yes, you have the right idea. A consequence of Gauss' law is that the net flux through any closed surface is proportional to the charge enclosed. A charge outside the closed surface cannot create a net flux through the surface.