A charged sphere of radius R has its origin at the origin of coordinates. The upper half of the sphere (z0) has a positive uniform volume charge density ρ, while the lower half (zR).

Question

A charged sphere of radius R has its origin at the origin of coordinates. The upper half of the sphere (z>0) has a positive uniform volume charge density ρ, while the lower half (z<0) has a negative uniform charge -ρ. Find the electric field produced at an arbitrary point on the z-axis above the sphere (z>R).

anonymous · Answer

Your best bet is to calculate the electric potential at that point and then find the electric field from there, although you could use a symmetry argument and work with the electric field all by itself -- I would advise against that though.

anonymous · Answer

Recall that
$$ \Phi(\vec{r}) = \int \frac{\rho}{|\vec{r}-\vec{r}'|} dV' $$
Where 
|dw:1378263082680:dw|