You have two metal spheres, one with radius 10 cm, the other 7 cm. They each possess a charge of 3 x 10-6 Coulombs. If you touch them together and let the charge come to equilibrium, how much will there be on each sphere?
The total charge Q=2q=2•3•10⁻⁶ C=6•10⁻⁶ C.
The total area of two spheres
A=4π(r₁²+r₂²) = 4π•149•10⁻⁴ m²
q₁=QA₁/A= 6•10⁻⁶•4πr₁²/A=
=6•10⁻⁶•4π•100•10⁻⁴/ 4π•149•10⁻⁴=4.027•10⁻⁶ C
q₂=QA₂A= 6•10⁻⁶•4πr₂²/A=
=6•10⁻⁶•4π•49•10⁻⁴/ 4π•149•10⁻⁴=1.973•10⁻⁶ C