# Electric field in a spherical shell

curiosissimo
Homework Statement:
We have a spherical shell with 2 radiuses $$R_1<R_2$$ The charge Q is distributed uniformly in the part of the sphere between R1 and R2. The inner space of the sphere ($$0<y<R_1$$) has no charge What is the electric field in the spherical shell?
Relevant Equations:
Gaussian theorem
So for the Gaussian theorem we know that $$\frac{Q}{e} = \vec E \cdot \vec S$$ Q's value is known so we don't need to express it as $$Q=(4/3)\pi*(R_2 ^3-R_1 ^3)*d$$ where d is the density of the charge in the volume. I've expressed the surface $$S=4\pi*x^2$$ where x is the distance of a point in the shell from the center of the sphere. So we simply get $$E=\frac{Q}{e*4\pi*x^2}$$ but it's wrong and I really don't know why. Thanks in advance!

## Answers and Replies

Homework Helper
Gold Member
Hello, curiosissimo. Welcome to PF.

Don't confuse the total charge of the shell with the charge enclosed by the Gaussian surface.

curiosissimo
curiosissimo
Hello, curiosissimo. Welcome to PF.

Don't confuse the total charge of the shell with the charge enclosed by the Gaussian surface.
Of course! What a silly mistake! Thank you very much!

berkeman