What is the mass of a sphere with uniform charge?

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The mass of a sphere with uniform charge density P, radius R, and levitating above an infinite sheet with surface charge density u can be determined by equating its weight to the electrostatic force acting on it. The sphere can be treated as a point charge due to its infinitesimal size relative to the infinite sheet. The gravitational force and electrostatic force equations must be rearranged to isolate mass on one side. Additionally, the influence of the sheet can be calculated using the method of mirror charges to accurately determine the electrostatic force. Understanding these principles is crucial for calculating the mass of the sphere in this scenario.
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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?
 
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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.
 
Be careful not to forget to take into account influence (hint: can be calculated by the method of mirror charges).
 
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