A conducting sphere has a radius of r = 6.2 cm and a net charge of q = 4 𝜇C. What is the electric potential of its surface?

Question

A conducting sphere has a radius of r = 6.2 cm and a net charge of q = 4 𝜇C. What is the electric potential of its surface?

Answer 1

By the Gauss Law and Gauss Theorem, q/ε₀ = –∫∇²φdv = –∮∇φ•da = –4πr²dφ/dr by spherical symmetry. Assuming φ → 0 as r → ∞, integrating the last equation gives φ = q/4πε₀r for r no less than the sphere diameter.