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 Guass'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:
[tex]\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}[/tex]
And the way to do the summation is by using the equation:
[tex]- \ \frac{Q}{4 \pi \epsilon_0 r}[/tex]
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.

 

[sardar]

I completely understand your confusion and frustration with this problem. Point charges and electrostatic potentials can be a difficult concept to grasp, especially without a solid foundation in electrodynamics. However, I can assure you that there is a simpler way to think about this problem.

First, it is important to understand that a sphere made up of multiple point charges can still be treated as a single point charge when calculating the electrostatic potential at a certain distance. This is because the individual charges are evenly distributed throughout the sphere and their effects cancel out, resulting in a net charge at the center of the sphere.

To determine the single charge value for the sphere, you can use the concept of electric dipole moment. This is a measure of the separation of positive and negative charges within a system. In this case, the sphere can be viewed as an electric dipole with equal and opposite charges at its center. The electric dipole moment can be calculated by multiplying the charge of each atom by its distance from the center of the sphere and summing them all together.

Once you have the electric dipole moment, you can use the formula for electric potential due to a dipole to calculate the electrostatic potential at a certain distance from the sphere. This formula takes into account the distance between the point of interest and the center of the dipole, as well as the strength of the dipole moment.

I hope this explanation helps to simplify the problem for you. It is important to remember that while the sphere is made up of individual charges, their combined effect can still be treated as a single point charge for the purpose of calculating electrostatic potential.