Methods in Physics NO. 1 : Image Method


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}


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