🧄Surface Force for Two Equal Charges

The electromagnetic field locally mediates the repulsive force between two equal charges ( $+ q$ and $+ q$ ) through tension. On the midplane ( $x^3=0$ ), the total electric field is purely radial ( $E _3=0$ ), meaning the field lines run parallel to the surface. This zero normal component dictates that the total surface force, calculated using the Maxwell stress tensor, results from the tension along these field lines, giving $F= -\frac{q^2}{4 \pi \varepsilon_0(2 d)^2} e_3$. This calculated force is attractive (pulling the two field regions together), and it perfectly balances the upward push that the lower charge exerts on the field, thereby satisfying the requirement for static equilibrium and validating the concept that the field, not just the charges, is a mechanical entity subject to forces.

Surface Force for Two Equal Charges | Proof and Derivationviadean on Notion