Electrical fields of spherical shells

[lowiqretard]

Hello,

I am in a calc 1 general physics 2 summer session class and missed the lectures on this due to sickness. I'm really confused on applying coulomb's and gauss's laws to find the electrical field of a sphere or outside a sphere. This is of both variable and constant charge densities. I've been really struggling on this and feel retarded.

What is the exact process I need to apply to come up with the electrical field E:

1. of a sphere of uniform charge density ρ = cst inside the entire sphere

2. of a sphere of uniform charge density ρ = cst outside the sphere on a spherical shell of outer radius r

3. of a sphere of variable charge density ρ = ƒ(inner radius) inside the entire sphere

4. of a sphere of uniform charge density ρ = ƒ(inner radius) outside the sphere on a spherical shell of outer radius r

I can provide sample problems if needed.

thank you

 

[Orodruin]

It is a simple matter of applying the divergence theorem for a sphere of any given radius.