[Physics] How to the potential on a cube’s surface replicate the potential of a point particle

electrostaticspotential

If i have a cube (either hollow, or an insulating solid) and i want its surface have a potential such that it looks like a point particle outside of the box does that mean the exact potential on the cube itself is the same as the potential of a point particle?

Best Answer

Yes, the uniqueness theorem guarantees it. If you find a solution in which the potential on the surface of the cube looks just like the potential of a point particle, then the potential outside the cube must be identical to that of a point particle since there is only one unique solution satisfying this this boundary condition. (Assuming no external charges, of course.)

Related Question