Electric field of half a spherical shell

[asi123]

Homework Statement

Hey guys.
I've been trying to solve this question using Gauss law but I can't think of a surface that can contain this thing.
Is there another way to solve this?

Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[CompuChip]

Maybe it helps to draw a picture... suppose that the symmetry axis is the z-axis. Consider an intersection in the (x, y) plane, i.e. a circle of radius r(z) at height z. Draw some electric field lines to a point on the z-axis... the symmetry will provide some cancellations. If you use an angle $\phi$ to parametrize the circle, then you can divide the circle into small segments of length $r(z) \, d\phi$ and write down the contribution to the E-field from each segment. Once you have that, all you have to do is sum (i.e. integrate) over phi.

Yes I know, it's a lot of work :sad: