- #1

jerro

- 7

- 0

## Homework Statement

You have two spheres. The first is centered at the origin and as uniform positive charge density ρ and radius R. The second is shifted up a distance d, and it has uniform negative charge density -ρ and radius R.

Find the E field in the region of overlap.

## Homework Equations

Gauss' Law

## The Attempt at a Solution

I first found an expression for the E field inside a single sphere.

∫E dA = [itex]\frac{Q}{\epsilon}[/itex]

E(4[itex]\pi[/itex]*[itex]r^{2}[/itex]) = [itex]\frac{\rho*(4/3)\pi*r^{3}}{\epsilon}[/itex]

E=[itex]\frac{\rho*r}{3\epsilon}[/itex]

Now, for extending the case to include both spheres.

I add the E field from one to the E field of the other, giving [itex]\frac{\rho*r}{3\epsilon}[/itex] - [itex]\frac{\rho*r}{3\epsilon}[/itex], which gives zero.

I'm not sure that this is correct, I'm feeling weary of r, the radius of the Gaussian surface, and whether it is the same for both spheres.