Answer to Question #133479 in Electricity and Magnetism for viccy

Question

how can we express electric field on conducting sphere.

Answer 1

Let the charge on the sphere be Q and the radius of the sphere be R.

We may apply the Gauss's law (see https://en.wikipedia.org/wiki/Gauss%27s_law) to the sphere. The total flux $\Phi$ through the surface of the sphere ($4\pi R^2$ ) is proportional to the total charge inside the sphere:

$\Phi = E \cdot S = E \cdot 4\pi R^2 = \dfrac{Q}{\varepsilon_0}$ . Therefore, the field of the sphere will be

$E = \dfrac{Q}{4\pi\varepsilon_0 R^2},$ where $\varepsilon_0$ is the vacuum permittivity (ε₀ = 8.8541878128(13)×10⁻¹² F⋅m⁻¹).

More detailed derivation can be found in farside.ph.utexas.edu/teaching/302l/lectures/node25.html for the negative charge.