# Electric field at centre of hollow half sphere

1. Jan 25, 2017

### Cocoleia

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I figured you could consider it as infinitely many rings? Here is what I did so far:

I feel like 0 is the wrong answer. Can anyone help me? Thanks.

2. Jan 25, 2017

### Staff: Mentor

For future posts: please try to type in your messages as it is difficult to impossible to read it on mobile devices.

3. Jan 25, 2017

### TSny

Your notation is confusing. The axis of the rings is the z-axis, but you use the symbol $x$ to denote the position of the center of a ring. Also, you appear to initially use the symbol $R$ for the radius of a ring, but then later use $R$ for the radius of the hemisphere. (The problem statement says the radius of the hemisphere is $a$.) Also, the symbol for the surface charge density as specified in the problem is $\rho_s$.

Nevertheless, your final integral looks correct except for the upper limit of integration. [Edit: Should your integration variable be $\theta$ or $\phi$ (if these symbols are defined according to the problem statement)?]

Last edited: Jan 25, 2017
4. Jan 25, 2017

### cnh1995

Everything looks fine except the limits of your final integral. Are you sure Φ varies from 0 to 2π?
Edit: TSny beat me to it while I was typing..