Electric field at the surface of a spherical conductor and the recalcitrant factor 1/2

The present article deals, once again, with the electric field behavior of a charged spherical conductor with emphasis on the value of the field on its surface. This value of the electric field on the surface of a spherical conductor has been discussed in some articles recently published in scientific journals and has conflicted some classic results, such as the fact that the electric field is discontinuous on the surface of a uniformly charged spherical conductor when admitting a superficial charge distribution. This article resumes the discussion, using the same models mentioned, showing an analysis of the search and interpretation of the insistent factor $\frac{1}{2}$ . The value of the field on the surface of a spherical conductor with uniformly distributed charge on its surface is not arbitrarily given by it. The mathematical behavior of the field depends on the model adopted.

Keywords:
electric field; charged sphere; discontinuity

Authorship

Gustavo Elia Assad ^**Endereço de correspondência: gustavo.elia.assad@gmail.com.

Universidade Federal da Paraíba, João Pessoa, PB, Brasil.Universidade Federal da ParaíbaBrasilJoão Pessoa, PB, BrasilUniversidade Federal da Paraíba, João Pessoa, PB, Brasil.

http://orcid.org/0000-0002-7780-0036

^*Endereço de correspondência: gustavo.elia.assad@gmail.com.

SCIMAGO INSTITUTIONS RANKINGS

Universidade Federal da Paraíba, João Pessoa, PB, Brasil.Universidade Federal da ParaíbaBrasilJoão Pessoa, PB, BrasilUniversidade Federal da Paraíba, João Pessoa, PB, Brasil.

Figures | Tables | Formulas

Figures (10)
Tables (1)
Formulas (24)

$\begin{array}{l} R_{1} = R - δ \\ R_{2} = R + δ \end{array}$	$E (R) = \frac{Q}{4 π ε_{0}} \frac{R^{1 + n}}{{(R + δ)}^{3 + n}} \frac{[1 - \frac{{(R - δ)}^{3 + n}}{R^{3 + n}}]}{[1 - \frac{{(R - δ)}^{3 + n}}{{(R + δ)}^{3 + n}}]}$	$\lim_{δ \to 0} E (R) = \frac{Q}{8 π ε_{0} R^{2}} \equiv \frac{σ}{2 ε_{0}}$
$\begin{array}{l} R_{1} = R - \frac{2 δ}{3} \\ R_{2} = R + \frac{4 δ}{3} \end{array}$	$E (R) = \frac{Q}{4 π ε_{0}} \frac{R^{1 + n}}{{(R + \frac{4 δ}{3})}^{3 + n}} \frac{[1 - \frac{{(R - \frac{2 δ}{3})}^{3 + n}}{R^{3 + n}}]}{[1 - \frac{{(R - \frac{2 δ}{3})}^{3 + n}}{{(R + \frac{4 δ}{3})}^{3 + n}}]}$	$\lim_{δ \to 0} E (R) = \frac{Q}{12 π ε_{0} R^{2}} \equiv \frac{σ}{3 ε_{0}}$
$\begin{array}{l} R_{1} = R - \frac{4 δ}{3} \\ R_{2} = R + \frac{2 δ}{3} \end{array}$	$E (R) = \frac{Q}{4 π ε_{0}} \frac{R^{1 + n}}{{(R + \frac{2 δ}{3})}^{3 + n}} \frac{[1 - \frac{{(R - \frac{4 δ}{3})}^{3 + n}}{R^{3 + n}}]}{[1 - \frac{{(R - \frac{4 δ}{3})}^{3 + n}}{{(R + \frac{2 δ}{3})}^{3 + n}}]}$	$\lim_{δ \to 0} E (R) = \frac{Q}{6 π ε_{0} R^{2}} \equiv \frac{2 σ}{3 ε_{0}}$