Why does charge distribute itself uniformly only on the surface of spherical conductors? I understand why charge does not distribute itself uniformly on the surface of a conductor of any other shape. I do not understand why charge distributes itself uniformly only on the surface of a spherical conductor. 
 A: The charge distributes uniformly on the surface of a spherical conductor (which is far from any other body) due to the spherical symmetry of the problem. There is no reason why it should accumulate at any location of the surface more than at any other location. Therefore it is distributed uniformly. Also, if it was distributed inhomogeneously, the electric fields would produce currents that redistribute the charge until there is no electric field inside and tangential to the surface.
A: By definition of a conductor (in equilibrium with no potential applied), the whole body must be at the same potential. That it must have no fields inside it otherwise the molecules will orient itself until their is no field inside it.
So Consider a solid spherical conductor. Take the spherical symmetrical Gaussian surface of radius less than the radius of the conductor.
Observe that the inside field must be zero by the above argument. So the net flux going through the Gaussian surface must also be zero. So there is no net charge inside the sphere.
This can be done for all Gaussian surfaces until we get to the surface, where we are no longer inside the conductor and Electric field can now exist.
Hence when you put charge on the conductor it goes to the outside.
PS- This type of reasoning can be put forward with a conductor of any shape.
