Electrostatic equilibrium: Difference between revisions
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A conductor is said to have reached electrostatic equilibrium when its charge distribution becomes stable. | |||
[[File:Electrostatic-induction.svg|500px|center]] | |||
For example, all conductors in the picture above have reached electrostatic equilibrium. | |||
== Properties == | |||
Consider a solid conductor $(S)$ at electrostatic equilibrium. | |||
By combination of [[Classical_mechanics#Newton's_2nd_law|Newton's 2nd law]] and [[Electric_charge#Electrostatic_force|Coulomb's law]], for any macroscopic charge $A$: | |||
$$\vec a = \frac{Q_A\vec E}{m}$$ | |||
By definition of electrostatic equilibrium, | |||
$$ | |||
\forall A \in (S), \vec a=0 \\ | |||
\therefore \vec E =0 \text{ for every point inside (S) (1)} | |||
$$ | |||
As a result, if conductor $(S)$ is charged, any charge must be destributed on the surface of $(S)$, $S(S)$, which creates an electric field on $S(S)$. | |||
This field must satisfy $\vec E \bot S(S)$ at all points. (3) Otherwise, the macroscopic charges would move along the surface. | |||
=== Summary === | |||
To summarise, the three properties for a conductor at electrostatic equilibrium are: | |||
# $\vec E_{internal}=0$ | |||
# charges may exist only on the surface of the conductor | |||
# on the surface, $\vec E =0 \lor \vec E \bot \text {surface}$ | |||
Latest revision as of 21:19, 1 October 2026
A conductor is said to have reached electrostatic equilibrium when its charge distribution becomes stable.
For example, all conductors in the picture above have reached electrostatic equilibrium.
Properties
Consider a solid conductor $(S)$ at electrostatic equilibrium.
By combination of Newton's 2nd law and Coulomb's law, for any macroscopic charge $A$:
$$\vec a = \frac{Q_A\vec E}{m}$$
By definition of electrostatic equilibrium,
$$\begin{gathered} \forall A \in (S), \vec a=0 \\ \therefore \vec E =0 \text{ for every point inside (S) (1)} \end{gathered}$$
As a result, if conductor $(S)$ is charged, any charge must be destributed on the surface of $(S)$, $S(S)$, which creates an electric field on $S(S)$.
This field must satisfy $\vec E \bot S(S)$ at all points. (3) Otherwise, the macroscopic charges would move along the surface.
Summary
To summarise, the three properties for a conductor at electrostatic equilibrium are:
- $\vec E_{internal}=0$
- charges may exist only on the surface of the conductor
- on the surface, $\vec E =0 \lor \vec E \bot \text {surface}$