Introduction of Electrostatics

Electrostatics is the part of the subject physics which deals with the phenomena and properties of stationary or sluggish electric charges.

Since classical antiquity, it has been recognized that various materials like ocher magnetize lightweight particles after chafing. Electrostatic phenomena happen from the forces that electric charges put forth on each other. Such forces are explained by Coulomb's law. Although electrostatically influence forces seem to be rather frail, the electrostatic force between e.g. an electron and a proton, which make up a hydrogen atom together, is about 40 orders of extent powerful than the gravitational force acting among them.

Coulomb's law

The basic equation of electrostatics is Coulomb's law which enlightens the force among two point charges. The magnitude of the electrostatic force among two points electric charges Q₁ and Q₂ is directly proportional to the product of the magnitudes of each charge and inversely proportional to the surface area of a sphere whose radius is equal to the distance among the charges:

where ε₀ = constant (vacuum permittivity or permittivity of open space), a defined value:

in  A²s⁴ kg^-1m^-3 or C²N^-1m^-2 or F m^-1.

Electric field

The electric at a point is defined as the force (in Newton's) per unit charge (in coulombs) on a charge at that point:

Or we rather say a charged entity in an electric field feels a force F=qE

From this definition and Coulomb's law, it tracks that the magnitude of the electric field E created by a test charge Q is:

The electric field produced by an allocation of charges given by the volume charge density is obtained by a triple integral of a vector function:

The value of the electric field depicts the force on a charged particle if it entered the electric field. An electric field line gives the direction of force on a positive charge in the electric field.

Gauss's law

Gauss' law says that "the entire electric flux through any closed hypothetical surface of any shape drawn in an electric field is proportional to the total electric charge enclosed within the surface".

Mathematically, Gauss's law takes the form of an integral equation:

Alternatively, in differential structure, the equation turns into

whereis the divergence operator.

Poisson's equation

The definition of electrostatic potential, joint with the differential form of Gauss's law (stated above), provides a relationship among the potential Φ and the charge density ρ:

This relationship is a type of Poisson's equation.

Laplace's equation

In the absence of unpaired electric charge, the equation turns into

which is Laplace's equation.

Electrostatic approximation

The validity of the electrostatic rough calculation rests on the assumption that the electric field is irrotational:

From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields:

Alternatively, electrostatics does not entail the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they should not change with time, or in the awful-case, they should change with time only extremely slowly. In several problems, both electrostatics and magneto statics may be required for precise predictions, but the coupling among the two can still be ignored.

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