# Surface Volume and Line charge densities, how to solve problems?

1. Jul 14, 2013

### turtieari

This question is a perfect example:

A solid sphere 25cm in radius carries 14microC, distributed uniformly throughout it's volume. Find the electric field strength a) 15cm b)25cm and c)50 cm from center.

I know that I need my gaussian surface and I also need
p=q/v where p is the (Qenclosed) in the equation: Qenclosed/epsilon=EA

Could someone help me understand what the charge densities are for. Do I have to subsitute Qenclosed for p or do I just use it as a clue that I need the volume?

Warmest regards,
ARi :"D

2. Jul 14, 2013

I don't think you actually need to use Gauss's law for this one, TBH. Since it's a sphere with uniform ρ, by the Shell Theorem, it acts like all the charge were centered at, well, the center. I'd solve using

E = q/(4πε₀r^2)

If you really want to use a Gaussian surface, since it's symmetrical:

qenc/ε₀ = EA -> E = 14µC/ε₀(4πR^2)

Where R is .15m+whatever the distance is from the sphere. Since the shell theorem comes from Gauss's Law, sort of, I guess they're actually the same answer, though.

Hope this helps.

3. Jul 14, 2013

### turtieari

The shell theorem is new to me. Maybe I don't know with that name. THANK YOU!

4. Jul 15, 2013