Two charged spheres A and B have equal radius R and respective uniform volume charge densities +ρ and −ρ. Their intersecting volume is uncharged, as shown. If the centres are O and O′ and Vₒ − Vₒ′ = ρR²/(nε₀), find n.
Physics · Mixed Chapter
JEE Mains

Question

Two charged spheres A and B have equal radius R and respective uniform volume charge densities +ρ and −ρ. Their intersecting volume is uncharged, as shown. If the centres are O and O′ and Vₒ − Vₒ′ = ρR²/(nε₀), find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Explanation: Treat the configuration as two superposed uniform charge distributions of densities +ρ and −ρ with their common overlap removed. Adding the potentials of the positive and negative spheres at the marked centres yields V at O−V at O′=ρR²/(3ε₀) for the separation shown; hence n=3. Geometry is taken from the supplied figure.