Methods in Physics NO. 1 : Image Method

27Dec07

Suppose that we have a grounded sphere made from a conductor and an electron far from the sphere. Let the radius of the sphere be $r$ and the beginning speed of the electron be $v$ orientated on the line in distance of $2r$ from the center of the sphere. The smallest distance between electron and the center of the sphere is $\frac{3}{2}r$

Calculate $v$ supposing to have everything else.

The solution is easy after the following observation:

A grounded sphere becomes an equipotentional surface. And the proper arrangement of the electric charge is equivalent to a single electric charge placed on the axis with the electron and the middle of the sphere in distance $x' = \frac{r^2}{x}$