But how do I calculate \bar{E} if I don't know my σ? It's like the chicken egg problem except that it's not what comes first that matters, but I need one to know the other. All I know unfortunately is the shape of the conductor and the total charge Q which according to the uniqueness theorum has...
How do I calculate the charge distribution on the surface of any asymmetric closed conducting surface? Is it possible for me to calculate the surface charge density 'σ' as a function of '\bar{r}' the position vector in a spherical co-ordinate system in space, provided I know that the conductor...