Explaining Electric Flux with Enclosed Charges

[brushman]

I under stand that electric flux is proportional to the charged enclosed but I don't get why.

Homework Statement

Consider the sphere with the charged enclosed:
[PLAIN]http://electron9.phys.utk.edu/phys136d/modules/m4/images/Image985a.gif

As you can see the area and electric field vectors are always parallel.

Now compare that situation to one exactly the same except the charge is moved towards the edge of the sphere (but still inside).

In the first situation the area and electric field are parallel to each other so will have the max value. In the second situation the angle is not always 0 degrees.

How can situation two have the same electric flux when it has smaller angles?

Homework Equations

flux = E dot A



Thanks

 

[tiny-tim]

hi brushman!

the flux is ∫∫ E.dA

that is the same as ∫∫∫ ∇.E dxdydz

and ∇.E = 0 in empty space …

so draw a small imaginary sphere with the charge as its centre … the flux through the surfaces of both spheres must be the same (since there's no charge between them)