Pre-Quantum Electrodynamics

Force is the same as case of two point charges: \[ {\bf F} = -\frac{1}{4\pi \varepsilon_0} \frac{q^2}{(2d)^2} \hat{\bf z} \label{Gr(3.12)} \] Energy is however not the same: for two point charges, (\ref{Gr(2.42)}) gives \[ W = -\frac{1}{4\pi \varepsilon_0} \frac{q^2}{2d} \label{Gr(3.13)} \] whereas for the single charge and conducting plane, \[ W = -\frac{1}{4\pi \varepsilon_0} \frac{q^2}{4d} \label{Gr(3.14)} \] Half: \(E^2\) integrated over half the space in (\ref{eq:Energy_as_int_E2}).