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: