Point Charges Composing A Sphere

[RockMc]

I have a quick question about understanding the theory behind point charges and electrostatic potentials. I've not had any classes in electrodynamics, so I lack a comfortable foundation to help me think about these problems.

I need to determine the electrostatic potential a certain distance from a charged sphere. I know you can view a sphere as a point charge and apply Gauss's Law, but the difference for me is that my sphere is made up of hundreds of individual charges composing this sphere. Each charge can be viewed as individual point charges and they all have the same value.

What I do not understand is how do I get a single charge value for the sphere.

I thought about taking the (Q/r) portion of Gauss's law and doing a summation over all the atoms, but with the amount of atoms making up the sphere this is unreasonable. Is there some simpler way to think about this problem?

 

[BruceW]

Right. So taking a summation is a possible way to solve the problem, believe it or not. But the summation is in the form of an integral, due to the huge number of atoms making up the sphere. The other way is to use Gauss' law, which is easier, but maybe less easy to understand in an intuitive way.

EDIT: to make it clear, when I say Gauss' law, I mean:
$$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}$$
And the way to do the summation is by using the equation:
$$- \ \frac{Q}{4 \pi \epsilon_0 r}$$
For each individual point charge in the (continuous) charged sphere, by doing an integral, keeping in mind that r will be different for each charge.

 

[RockMc]

Ok, I believe I understand now! I think I was confusing myself with viewing the sphere as a point charge made of point charges, but Gauss's Law allows it to work that way.

Thank you for the help!

 

[BruceW]

no worries, glad that I was of help.