# What is the mass of a sphere with uniform charge?

The sphere has radius R, and uniform volume charge density P. This sphere remains stationary (levitates) when placed above an infinite sheet of paper with a uniform surface charge density u. What is this sphere's mass?

The sphere can be replaced with a point charge (the charge and mass of the sphere).

The weight of the sphere is equal to the electrostatic force between the sphere and the sheet when the sphere is levitating. Because the sheet is infinite the sphere is infinitessimal and is therefore a point. Write the equation for the electrostatic force and for the gravitational force and rearrange to give mass on one side of the equation and everything else on the other.

vanhees71