A necessary and sufficient condition for the electrostatic equilibrium between two or more conductors is: they must have the same electrical potential.

The electrostatic equilibrium is characterized by the absence of electrical current from one conductor to the other.

## Conductors in Electrostatic Equilibrium

Properties:

• The electrostatic equilibrium is characterized by the absence of orderly movement of electric charges.
• The electric field inside an electrified conductor is zero (otherwise, currents arises).
• The electric charges excess, positive or negative, are distributed on the surface (electrostatic shield).
• The inner region of the conductors has constant electric potential.
• The electric field vectors are perpendicular to the outer surface of the electrified conductor.
The Power of Sharp Edges:
The charge density (charge per unit area) is greater at points of high curvature, i.e., a smaller radius. This means that the electric charges are distributed more densely in sharp regions. This is the principle of operation of the lightning rod.
Dielectric Breakdown:
The maximum quantity of charges which can be in a conductor is limited. With very intense electric fields, the charges can ionize the molecules in the surrounding. When the surrounding medium becomes conductor of electricity, the conductor immersed in it is discharged. When this occurs, we say that there was disruption of the dielectric medium.
Dielectric Strength:
The dielectric strength is the value of the electric field in which the dielectric breakdown of a certain medium occurs. In atmospheric air the dielectric strength is: $$E_{max} = 3 \times 10^6 \frac{V}{m} = 3,000,000 \frac{V}{m}.$$