Question

Verufy that the electric field satisfies the 3rd rule of conductors in electrostatic equilibrium

A metal sphere of radius R has charge Q and it's placed far away from any other charges or electric fields, so that charge Q is uniformly distributed over the surface of the sphere. Verify that electric field E near the surface of the sphere and surface charge density sigma satisfy the "3^rd rule of conductors in electrostatic equilibrium", i.e. E = sigma/epsilon_0

Answer 1

3rd rule of conductors says " The electric field just outside the surface of an isolated conductor is perpendicular to the surface and has a magnitude equal to σ/εo, where σ is the local surface charge density."

So, from gauss's law for a metal sphere given,

Ex4 $\pi$ R² = Q/ $\varepsilon$ _o => E= (Q/4 $\pi$ R²)/ $\varepsilon$ _o = $\sigma$ / $\varepsilon$ _o

and here, E is perpendicular to surface