GITAM, Department of Engineering Physics
er = e / e0
It has no units and it is a measure of the electrical polarisation in the dielectrical material.
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If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. An applied electric field will polarize the material by orienting the dipole moments of polar molecules. This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure. The dielectric must be a good electric insulator so as to minimize any DC leakage current through a capacitor. |
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Polarization Vector, P
The total effect of an electrical field on a dielectric material is called the polarization of the material
To understand that better, lets look at the most simple object we have: A single atom (we do not even consider molecules at this point).
We have a positively charged nucleus and the electron "cloud". The smeared-out negative charge associated with the electron cloud can be averaged in space and time, and its charge center of gravity than will be at a point in space that coincides exactly with the location of the nucleus, because we must have spherical symmetry for atoms.
If we now apply an electrical field, the centers of charge will be separated. The electron cloud will be pulled in the direction of the positive pole oft the field, the nucleus to the negative one. We may visualize that (ridiculously exaggerated) as follows:
The center of the positive and negative charges q (= z ˇ e) are now separated by a distance x, and we thus induced a dipole moment m which is defined by
m = q ˇ x
It is important to understand that m is a vector because x is a vector. The way we define it, its tip will always point towards the positive charge. For schematic drawings we simply draw a little arrow for m.
The magnitude of this induced dipole moment is a property of our particular atom, or, if we generalize somewhat, of the "particles" or building blocks of the material we are studying.
In order to describe the bulk material - the sum of the particles - we sum up all individual dipole moments contained in the given volume of the material and divide this sum by the volume V. This gives us the (volume independent) polarization P of the material. Notice that we have a vector sum!.
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S m V |
= |
<m> ˇ N V |
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With <m> = average vector dipole moment; NV = density of dipoles (per m3).
P thus points from the negative to the positive charge, a convention opposite to that used for the electrical field.
The physical dimension of the polarization thus is C/m2; (Coulomb per square meter). i.e. the polarization has the dimension of an area charge, and since m is a vector, P is a vector, too.
It is important to realize that a polarization P = 0 does not mean that the material does not contain dipole moments, but only that the vector sum of all dipole moments is zero.
If we measure the polarization of a material, we usually find a linear relationship between the applied field E and P, i.e.
P = e0 ˇ c ˇ E
Electric Flux Density, D
Historically, inside materials, the electrical field strength E was (and still is) replaced by a vector D called the electrical flux density, which is defined as
D = er ˇ e0 ˇ E
and er was (and still is) called the (relative) dielectric constant (DK) of the material (the product er ˇ e0 is called the permittivity, e), i.e.
D = e ˇ E
D is supposed to give the "acting" flux inside the material.
The dielectrical flux D in a dielectric caused by some external field Eex is the flux D0 in vacuum plus the polarization P, i.e.
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D = D0 + P |
= e0 ˇ E + P |
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From this we can get
|
P E |
= | e - e0 | = | e0 ( er - 1 ) |
Electric Susceptibility, c
If we measure the polarization of a material, we usually find a linear relationship between the applied field E and P, i.e.
P = e0 ˇ c ˇ E
where the constant c is referred to as the electric susceptibility and is a characteristic of every dielectric.
|
P e0 E |
= |
er - 1 |
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The relative dielectric constant er is simply the dielectric susceptibility c plus 1.
| er = | 1 + c |
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