Electric Fields and excess charge vs charge

[jlatshaw]

Hello,
I have a few questions (with regards to conducting hollow spheres) .

1: What is the difference between a charge in the sphere and an excess charge coming out of the sphere or the charge resting on the outside of a sphere?

2: Image a conducting sphere that has a shell of a small thickness R (like 1 cm for example, not infinitely small though). If there is a negative charge in the center of this sphere (-Qcenter)and a positive excess charge on the outside of the sphere(+Qexcess), then my E field at any given point outside or the R radius of the sphere should have an electric field of
E=(k*(Qexcess + Qcenter))/(r^2) where r is distance from center of the sphere. (r>R)

3: My question is why do we take add Qexcess + Qcenter for the total charge even though Qexcess is negative? And what is the difference between the excess charge on the surface and the charge at the center?

4: Also imagine two concentric conducing spheres that are hollow and the thickness of their shells is very very small.

The shell on the inside has an negative excess charge of -Qexcess, and we are given the value of the electric field at r distance away from the center of both of these shells (this r is greater than the radius of both the shells). We are then told to find the charge on the surface of the external shell. We can use:
E = (kq)/r^2
q = (E*r^2)/k
ok so that is the charge on the surface of the shell, however it is completely unrelated to the external charge on the interior of the shell, Why? What do they mean by "charge on the surface of the shell?"

5: I guess most of my questions are just really begging for a clear definition of (especially with regards to hollow sphere):
Point Charge:
Excess Charge:
Charge on the surface:

6: What is a good rule to remember to help me better understand the differences between these and what is going on in the equations?

Thank you for any help,
-James

 

[Doc Al]

The key is to realize that the field within the conducting material (at least in the electrostatic case, which is what concerns us here) must always be zero.

So, image a spherical conducting shell. If there is charge +Q placed within it, there must be a charge of -Q induced on its inner surface. And if the shell has no net charge, that means its outer surface has a charge of +Q. As far as the field outside the shell goes, it is the same as that of a charge of +Q at its center.

Any net charge on the shell just adds to the charge on its outer surface.