Source: High school physics (Chinese)
Problem Sets:
Problem
An isolated conducting sphere carries charge $+Q$.
- In what direction is the electric field at the surface of the sphere? Is $Q$ uniformly distributed on the surface? Is the surface an equipotential? What is the field at any interior point $P$?
- If another charged body is brought close, at the new electrostatic equilibrium: is the surface charge still uniformly distributed? In what direction is the surface field? Is the surface still an equipotential? Does the field at the interior point $P$ change?
Isolated: surface field outward and perpendicular to the surface; $Q$ uniform; surface is equipotential; $E_P = 0$ inside. With external body: distribution non-uniform; surface field still perpendicular; still equipotential; $E_P = 0$ inside (unchanged).
For an isolated conductor in electrostatic equilibrium: (i) the surface field is perpendicular to the surface, since any tangential component would drive surface currents; (ii) by symmetry, $Q$ is uniformly distributed on the isolated sphere; (iii) the conductor is at one potential, so the surface is equipotential; (iv) inside the conductor, $E = 0$.
When another charged body approaches, induction redistributes the free charge on the sphere but the four equilibrium properties become: the distribution is no longer uniform (induced charges concentrate near the external body); the surface field is still perpendicular to the surface (still equilibrium); the conductor remains a single equipotential; and inside the conductor $E$ is still zero.