Two spheres with uniform surface charge density have combined charge ?

Question

two shpere with uniform surface charge density, one with a radius 7.2cm and the other with a radius 4.7cm are separated by center to center distance of 33cm. The spheres have combined charge of 55 mirco C and repel one another with a F= .75N. That is surface charge density on each sphere?

Answer 1

If the surface density is uniform, the force is as if all the charge were at the enter of the sphere.

The force is given by Coulomb's law:

http://en.wikipedia.org/wiki/Coulomb's_l...

which gives you the product of the charges. You also have the sum of the charges. So you can solve for the two charges

If a + b = X and ab = Y, then a + Y/a = X or

a^2 - aX + Y = 0

so you have a quadratic equation.

Given the total charge and the radius of the sphere, you can compute the sphere's area and hence the surface charge density.