At a conductor surface, what are the boundary conditions on the electric field immediately outside the surface?

At a conductor surface, what are the boundary conditions on the electric field immediately outside the surface?

• A. E_perp outside = 0; E_tangential outside = σ_free/ε0; inside E = 0
• B. E_perp outside = σ_free/ε0; E_tangential outside = 0; inside E = 0
• C. E_perp outside = σ_free/ε0; E_tangential outside = σ_free/ε0
• D. E_perp outside = -σ_free/ε0; E_tangential outside = 0; inside E = 0

Answer: (B)

At a conductor surface, the field inside is zero in electrostatics because free charges rearrange to cancel any internal field. The normal component of the electric field just outside the surface is set by the surface charge density via Gauss’s law: E_perp_out - E_perp_in = σ_free/ε0. Since E_perp_in = 0, we get E_perp_out = σ_free/ε0. The tangential component of E just outside a conductor must be zero; any nonzero tangential field would drive surface currents, which isn’t present in a static situation. Therefore, E_tangential outside = 0. Putting it together: E_perp outside = σ_free/ε0, E_tangential outside = 0, and inside E = 0. This matches the described relations.

At a conductor surface, the field inside is zero in electrostatics because free charges rearrange to cancel any internal field. The normal component of the electric field just outside the surface is set by the surface charge density via Gauss’s law: E_perp_out - E_perp_in = σ_free/ε0. Since E_perp_in = 0, we get E_perp_out = σ_free/ε0. The tangential component of E just outside a conductor must be zero; any nonzero tangential field would drive surface currents, which isn’t present in a static situation. Therefore, E_tangential outside = 0. Putting it together: E_perp outside = σ_free/ε0, E_tangential outside = 0, and inside E = 0. This matches the described relations.