What is the net electric field at a point between two charged spheres?

[Oijl]

Homework Statement

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?

Homework Equations

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.

 

[Redbelly98]

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.

That's a good start to this problem.

But then I realized that the electric field from the first sphere will affect the charge on the point because it'll do a little canceling out of the field from the second sphere.

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

I do believe I should create a Gaussian surface somewhere, but I'm not sure where.

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

 

[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.

 

[Redbelly98]

But I can't just calculate the electric field due to each sphere and use the principle of superposition,...

Yes you can.

...because the electric field at the given point due to the first sphere is zero because that point is enclosed by said sphere.

That makes the problem even easier.