Kevin Zhou — E&M I Problem 1 · Kevin Zhou #E1.1

Physics · electromagnetism

Problem

Problem 23. Show thatany surface ofcharge density σ with electric fields E and E immediately 1 2 on its two sides experiences a force σ(E +E )/2 per unit area. (This is a generalization of the 1 2 example above, where one side was inside a conductor.)
Intuitive explanation

The key insight is that the force on a surface charge comes from the average of the fields on either side—not from the field it creates itself. Imagine a thin pillbox straddling the surface: the field discontinuity E1−E2=σ/ϵ0E_1 - E_2 = \sigma/\epsilon_0 tells you how much charge is there, but the force depends on what field acts on that charge. The field acting on the surface layer is the average of its two neighbors, since the surface's own field can't exert force on itself. This elegant result shows why conductors (where Einside=0E_{\text{inside}} = 0) experience outward electrostatic pressure.

Intuitive explanation

The key insight is that the force on a surface charge comes from the average of the fields on either side—not from the field it creates itself. Imagine a thin pillbox straddling the surface: the field discontinuity E1−E2=σ/ϵ0E_1 - E_2 = \sigma/\epsilon_0 tells you how much charge is there, but the force depends on what field acts on that charge. The field acting on the surface layer is the average of its two neighbors, since the surface's own field can't exert force on itself. This elegant result shows why conductors (where Einside=0E_{\text{inside}} = 0) experience outward electrostatic pressure.

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