Buck minster fullerene is a molecule of 60 carbon atoms arranged like the stitching on a soccer-ball. It may be approximated as a conducting spherical shell of radius R = 3.5 . A nearby electron would be attracted, according to Prob. 3.9, so it is not surprising that the ion exists. (Imagine that the electronon average-smears itself out uniformly over the surface.) But how about a second electron? At large distances it would be repelled by the ion, obviously, but at a certain distance r (from the center), the net force is zero, and closer than this it would be attracted. So an electron with enough energy to get in that close should bind.
Prob. 3.9
In Ex. 3.2 we assumed that the conducting sphere was grounded (V = 0). But with the addition of a second image charge, the same basic model will handle the case of a sphere at any potential V0 (relative, of course, to infinity). What charge should you use, and where should you put it? Find the force of attraction between a point charge q and a neutral conducting sphere.
Example 3.2
A point charge q is situated a distance a from the center of a grounded conducting sphere of radius R (Fig XXXXXXXXXXFind the potential outside the sphere.
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