Electric Potential.
An electrostatic field may be described by different, but equivalent terms:
It is irrotational, |
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The integral |
Edl 0 |
vanishes |
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B |
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The integral |
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solely depends |
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A |
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on the points A and B but not on the particular |
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path taken from A to B. |
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Definition of the potential: U (B) U ( A) E |
dl ; |
E U |
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A
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Work in the Electric Field.
The field performs work on charges
Conversely, to move the charge against the field requires one to do work.
The force, |
F QE |
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B |
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The work |
A Fdl |
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or |
A Q Edl |
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A |
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A Q U A U B |
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For infinitely remote point A: |
A Q U B |
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The work against field forces: A Q U B ; this work increases the field energy
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Dielectric polarization.
Dielectric materials are polarized when an electric field is applied to them. As a result, electric displacement becomes greater than under the free space condition:
D 0 E P
The polarization is defined as the dipole moment per unit volume.
In isotropic and linear materials, the polarization is directly proportional to the electric field and the proportionality constant does not depend on the field
P0 E
is the susceptibility of dielectric material.
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Dielectric material characteristics.
In the linear dielectric material the field |
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D 0 E 0 E |
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intensity is proportional to the displacement |
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D E |
0 1 |
is the dielectric permittivity (dielectric constant) |
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r |
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is the relative dielectric permittivity (dielectric constant) |
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0 |
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In the case of extremely high electric field the electrons will accelerate and collide with molecular lattice structure, which causes permanent damage to the material. This phenomenon is known as dielectric breakdown.
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Properties of dielectric materials.
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Poisson’s and Laplace’ s equations.
E U |
In the absence of free charges D 0 |
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D E |
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For the linear dielectric const |
U 0 |
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U 0 |
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Laplace’s equation
In general case
For the linear dielectric
U
U
Poisson’s equation
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