# Potential of all space from sphere

1. Homework Statement
Consider a sphere or radius a. The top hemisphere has a uniform charge density $$\sigma$$, the bottom has -$$\rho$$. Calculate the electric potential in all space.$$\sigma$$

2. Homework Equations
Laplace's Equation:
$$\nabla$$$$^{2}$$=-4$$\pi\sigma$$

Potential (solved from Laplace's Equation):
V=$$\int\frac{\rho(r)}{r}$$d$$\tau$$

3. The Attempt at a Solution
I solved laplace's equation to get the potential is the integral over rho/r. I want to integrate from 0 to a, and then a to R; where R is some arbitrary point. I want to just plug in [txt]\sigma[txt] times a, for the charge, and integrate it over r.

I'm not sure how to treat the -[txt]\sigma[txt]. Any ideas?

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