# Point charge moving towards a conducting plane

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by:

$\Delta t= \frac{\pi d} {q} \sqrt{2\pi\epsilon_0md}$

I can't seem to start this one. I'm assuming I need to start by finding the force by the charge as a function of $z$, and setting it equal to $\frac{md^2z}{dt}$ giving a differential equation. The diff eq. seems hard to solve, but a hint I recieved was to multiply both sides by $\frac{dz}{dt}$, but I don't see how this simplifies the problem.

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–  santa claus Feb 21 '13 at 19:35
use the method of images to find the force. then the trick is to write $\frac{d^2 z}{dt^2}$ as $\dot{z} \frac{d \dot{z}}{dz}$. –  nervxxx Feb 22 '13 at 1:31