Very difficult series circuit question

[rollwiththis]

Homework Statement

so basically there is a total of 2008 identical resistors and 2009 identical charged spheres. The spheres have a total charge of Q. I’m trying to find out what the radius of one of these spheres is.

Homework Equations

integral (E dot A) = (sum of all q's)/(Eo)

The Attempt at a Solution

Now I know i have to use a combination of Gauss's law and series circuits but I'm not actually sure where to begin. Any help would be greatly appreciated. Thanks in advance.

 

[Jhero]

Hello there,

Thank you for your post. It seems like you have a very interesting problem to solve! Here are some steps that you can follow to find the radius of one of the spheres:

1. Start by setting up a closed surface around one of the spheres. This surface should enclose only one sphere and none of the others.
2. According to Gauss's law, the electric flux through this surface should be equal to the net charge enclosed by the surface divided by the permittivity of free space (Eo).
3. You can calculate the net charge enclosed by the surface by summing up the charges of all the spheres within the surface. Remember that the spheres are identical, so each one has the same charge (Q).
4. Now, you can use the formula for the electric flux (E dot A) to find the electric field at the surface of the sphere. The electric field should be constant throughout the surface.
5. Finally, use the formula for electric field inside a sphere (E = Q/(4πEor^2)) to find the radius (r) of the sphere.

I hope this helps you get started on your problem. Let me know if you have any further questions or need clarification on any of the steps. Good luck!