Final answer:
The charge probability density for a uniformly accelerating charge differs from that of a non-accelerating charge due to radiation of energy. The potential outside a uniformly charged sphere is the same as that of a point charge but differs within the sphere. Non-uniform charge distribution within a sphere doesn't affect external potential, which only depends on the total charge.
Step-by-step explanation:
The charge probability density of a uniformly accelerating charge is different from a charge that isn’t accelerating. When a charge accelerates, it radiates energy in the form of electromagnetic waves, which alters the distribution of the electromagnetic fields around it. In contrast, a stationary or uniformly moving charge (not accelerating) has a static or unchanging electromagnetic field. The potential due to a uniformly charged sphere is the same as that of a point charge at any point outside the sphere (external to the surface). However, inside the sphere, the potential differs from that of a point charge due to the volume distribution of the charge.
For a non-uniformly charged sphere, the potential can still be equivalent to that of a point charge at points outside of the sphere. The potential at any external point only depends on the total charge of the sphere, not on how it's distributed within the sphere. Gauss's Law helps explain this phenomenon, as it relates to the electric flux that penetrates a closed surface and shows that it is only dependent on the enclosed charge.
When comparing uniform charged geometries, such as a uniformly charged rectangle versus a disk, the charge distribution over these shapes would affect the electric field and potential in the space around them. The probability density, electric potential, and forces acting on charges within these fields would exhibit different characteristics depending on the geometry of the charge distribution.