Electric field outside charged sphere¶

The electric field outside of a charged sphere behaves as is the sphere were a point charge, i.e. its magnitude is inversely proportional to the square of the distance to the center of the sphere. However, due to the Gauss’s law, on the inside the electric field is exactly zero.

Notation:

\(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.

Conditions:

The sphere is thin, i.e. its thickness approaches zero.

Links:

Wikipedia, “Spherical volume”.

electric_field_strength¶

electric_field_strength.

Symbol:: E
Latex:: \(E\)
Dimension:: voltage/length

charge¶

Total charge of the sphere.

Symbol:: q
Latex:: \(q\)
Dimension:: charge

distance¶

euclidean_distance to the center of the sphere.

Symbol:: d
Latex:: \(d\)
Dimension:: length

law¶

E = q / (4 * pi * epsilon_0 * d^2)

Latex:: \[E = \frac{q}{4 \pi \varepsilon_0 d^{2}}\]