= Falling charge above a grounded conducting plane
{title2=$T=\pi\sqrt{2\pi\varepsilon_0md^3}/|q|$}
A real charge of height $z$ has a reflected <image charge> at $-z$. Its acceleration is $\ddot z=-\kappa/z^2$, with $\kappa=q^2/(16\pi\varepsilon_0m)$. Released from rest at height $d$, its ideal-model arrival time is
$$
T=\frac{\pi d^{3/2}}{2\sqrt{2\kappa}}.
$$
The image follows the instantaneous reflected position. The induced-charge energy carries one-half the full real-image pair interaction factor, consistent with this force.
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