❓Force on Charges and Static Equilibrium

The three pages explains how the Coulomb force is calculated for two equal charges, q, separated by a distance of 2d. The force, $\vec{F}{\text{Coulomb}}$, exerted by one charge on the other is a repulsive force with a magnitude given by the formula: $\left|\vec{F}{\text{Coulomb}}\right| = \frac{q^2}{4\pi\epsilon_0 (2d)^2}$. For a charge located at $x_3 = -d$ (the lower charge) due to a charge at $x_3 = d$ (the upper charge), the vector force points in the $-\vec{e}_3$ direction (downward). This result is crucial for verifying the computation of the surface force on the electromagnetic field in a static equilibrium scenario, where the surface force is expected to be equal in magnitude and direction to the Coulomb force on the charge.

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