Electrostatic stability and instability of N equal charges in a circle

✍ Scribed by Alexander A. Berezin

• Book ID: 103023169
• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 223 KB
• Volume: 123
• Category: Article
• ISSN: 0009-2614
• DOI: 10.1016/0009-2614(86)87015-4

✦ Synopsis

The Coulomb energy of N equal charges placed in a circle is calculated. Contrary to the common belief, the configuration with the minimum energy does not always correspond to the symmetrical placement of all N charges on the circumference. This is true only for N < 11; for N > 11 the configuration with N -1 charges on the circumference and one (Nth) charge in the center of the circle is energetically more preferable. Therefore, for N > 11 there will be a spontaneous "electrostatic ejection" of the Nth electron from the circumference into the center of the circle. The related problem of the equilibrium configuration of N point charges on a sphere is also briefly discussed.