# Gauss' Law w/ two spheres

1. Sep 13, 2009

### Oijl

1. The problem statement, all variables and given/known data
Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers are separated by L = 14 cm. What are the magnitude and direction of the net electric field at x = 2.0 cm?

2. Relevant equations

3. The attempt at a solution
I tried to just ignore the first sphere and use E = q / (4 pi epsilon0 r^2), taking q to be the full charge of the second sphere acting as if it were centered at the sphere's center. But then I realized that the electric field from the first sphere will affect the field on the point because it'll do a little canceling out of the field from the second sphere. I do believe I should create a Gaussian surface somewhere, but I'm not sure where.

Last edited: Sep 14, 2009
2. Sep 13, 2009

### Redbelly98

Staff Emeritus
That's a good start to this problem.

The electric field will not affect the charges. Since the shells are non-conducting, the charges are fixed in place.

No, just calculate the electric field for each sphere alone, as you mentioned above.

3. Sep 14, 2009

### Oijl

But I can't just calculate the electric field due to each sphere and use the principle of superposition, because the electric field at the given point due to the first sphere is zero because that point is enclosed by said sphere.

4. Sep 14, 2009

### Redbelly98

Staff Emeritus
Yes you can.

That makes the problem even easier.