Question

Electric field due to a hemisphere at a distance x from the centre ( x> R) On the axis of hemisphere.

Answer 1

Hemisphere is conducting and uniformly charged.

Answer 2

I first derived the electric field from a disk to a point that is distance x away from the center of the disk.

s = surface density = Q/A
ep = permitivity of free space constant
r = radius of sphere
R = radius of disk

I found this to be [s/(2ep)]*[1 - x/sqrt(x^2 + R^2)]

Now I have to integrate this from X - R to X + R. But I cannot figure out how to express the radius of the disks in terms of the sphere radius without introducing more variables (ie angle variable).

I am also confused as to how exactly to correlate surface density with volume density.

I wish to use Coulomb's Law and not Gauss'.

Answer 3

You can try to get electric field at x for a circular ring, and then integrate it for the whole hemispherical bowl.