What Exactly is the Electric Field at the Surface of a Charged Conducting Sphere?
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In the presently available literature, one finds distinct results for the electric field at the surface of a charged conducting sphere. In most textbooks, only a simple model is presented in which the electric field leaps from zero (inside the sphere) to a maximum value (just outside the sphere), as follows from Gauss’s law. For points exactly at the surface, the charge surrounded by the Gaussian surface becomes ambiguous, and this law is inconclusive. In this paper, by treating the spherical surface as a series of rings, it is shown that that field evaluates to half the discontinuity mentioned above, a result which agrees with more elaborate microscopic models.
KeywordsElectric field charged conductors Gauss’s law half-factor charged sphere electrostatics
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- D C Giancoli, Physics–Principles with Applications, 7th ed. Prentice-Hall, Upper Saddle River-NJ, pp.464–465, 2014.Google Scholar
- R A Serway and R J Beichner, Physics for Scientists and Engineers, 8th ed. Brooks/Cole, Belmont-CA, pp.699–702, 2010.Google Scholar
- D J Griffiths, Introduction to Electrodynamics, 3rd ed. Prentice Hall, Upper Saddle River-NJ, Sec. 2.5.1., 1999.Google Scholar
- A Macêdo, Eletromagnetismo, Guanabara, Rio de Janeiro, Brazil, p.136, Ex.3.3.7., 1988Google Scholar
- D Halliday, R Resnick and J Walker, Fundamentals of Physics, 10th ed. Wiley, New York, pp.675–676, 2014.Google Scholar
- H D Young and R A Freedman, Sears & Zemansky’s University Physics, 14th ed., Pearson, San Francisco-CA, pp.734–735, 2016.Google Scholar
- A F Kip, Fundamentals of Electricity and Magnetism, 2nd ed. Mc Graw-Hill, New York, pp.49–52, 1969.Google Scholar
- E F Oliveira, J L C Robortella and A A Filho, Física, Vol.3, 7th ed. Ática, Sa˜o Paulo, Brazil, pp.273–274, 1992.Google Scholar
- F Ramalho Jr., N G Ferraro and P A Toledo Soares, Os fundamentos da física, Vol.3, 8th ed. Moderna, S˜ao Paulo, Brazil, pp.75–78, 2008.Google Scholar
- C T Shigekiyo, K Zyamamoto and L F Fuke, Os alicerces da Física, Vol.3, 14th ed. Saraiva, S˜ao Paulo, pp.91–92, 2007.Google Scholar
- G Bruhat, Curso de Física Geral, Vol.1: Eletricidade, 7th ed. Difus˜ao Européia do Livro, S˜ao Paulo, pp.74–75, 1961.Google Scholar
- E M Purcell and D J Morin, Electricity and Magnetism, 3rd ed. Cambridge University Press, New York, pp.30–32, 2013.Google Scholar
- J D Jackson, Classical Electrodynamics, 3rd ed. Wiley, New York, pp.19–22, 1999.Google Scholar
- A Gaspar, Física, Vol.3, 2nd ed. Ática, Sa˜o Paulo, pp.40–42, 2012.Google Scholar
- G E Assad, Electric Field ‘on the surface’ of a Spherical Conductor: An Issue to be Clarified, Rev. Bras. Ens. Fís., Vol.34, p.4701, 2012.Google Scholar
- S Ganci, A Little Subtlety on an Electrostatic Problem, Rev. Bras. Ens. Fís., Vol.30, p.1701, 2008.Google Scholar