Calculating Electric Potential at the Center of a Half Spherical Shell

[hellojojo]

Hey guys,

I have a question regarding fields. I hope you guys can guide me to the right answer!

The question states:
A charge Q = 42 nC is uniformly distributed over a half spherical shell of radius R = 48 cm.

What is the potential at the center?

I didn't learn Gauss's Law in class but I have kind of a working knowledge of what could be done?

SO i considered the equations: V=kq/r^2 and V=kq/r

I'm not sure which one to use, however I did use both equations. Both equations have me the wrong answer. But then I realized in order to use those equations the charge distribution has to be uniform all over the sphere, but this is only half a sphere, so these equations probably won't work-- unless I tweak them some how?

Please help?

 

[blue_leaf77]

V=kq/r^2 and V=kq/r

This is for the potential from a point charge. If the charge is distributed over a volume (or surface in our problem), you can picture it as an ensemble of point charge. The potential of the charge distribution is then the sum of potential due to the infinitesimal charge element constituting the distribution. You may want to know the solution of Poisson equation in regard with the potential of arbitrary charge distribution.

 

[rude man]

Take a differential area on the hemisphere dA. You know the surface charge density (right?) so you know the charge on dA. Now integrate over the surface. Note that r is constant over the entire integration.

 

[tommyxu3]

V=kq/r^2

This must be the magnitude of the electric field a static charge makes instead of its potential, or you use V to present again?