At the microscopic level, these bound charges can be displaced by an external electric field and result in induced electric dipoles. These induced electric dipoles are pairs of positive and negative charges that in some way align with the electric field.
Capacitors and Dielectrics
This results in an electric field inside a dielectric material that is different from that of free space. To get a macroscopic description of this phenomenon, it is convenient to introduce a polarization vector field , and a polarization charge density,. They are related by:. The polarization effects locally modify the electric field on the inside of a material according to:.
Based on this, a new fundamental quantity can be introduced. The electric displacement field, , is defined as:. To fully describe electrostatics phenomena, the condition that the electric field is irrotational Faraday's law still needs to hold. Since this condition is encoded in the electric potential, the equations of electrostatics can be combined into a single equation:.
Theory of Electric Polarization - 2nd Edition
The field around an object of higher permittivity than its surroundings. The images show a dielectric object, , surrounded by air, , between two capacitor plates not shown. The top and bottom electrodes have a positive and negative electric potential, respectively. The image to the left shows the magnitude of the electric field, , in color and its direction with arrows. The image to the right shows the magnitude of the electric displacement field, , in color and its direction with arrows.
Red and blue represent a high and low magnitude value, respectively. The field around an object of lower permittivity than its surroundings. The images show an air cavity, , surrounded by a dielectric material, , between two capacitor plates. In electrostatics, one can frequently assume that the material is linear.
This means that the polarization vector field is proportional to the electric field:. Combine this with the relationship between and :. This implies that for certain materials, the and fields may not be perfectly aligned. Using the electrostatic potential, the fundamental equation for electrostatics in linear materials is:.
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Gauss's law and Faraday's law can be seen as specifying conditions on the divergence and curl of the electric field, respectively. According to Helmholtz's theorem, this determines the electric field up to a constant. As a side note, this unknown constant is what ultimately makes it necessary to specify a ground level for the electric potential.
At material interfaces, the divergence condition implies a condition on the normal component of the field and the curl condition implies a condition on the tangential component of the field. Material interfaces represent discontinuities, and to more easily understand what conditions to impose on boundaries, the corresponding integral forms are usually used. The boundary formulations are then derived by taking the limit of a shrinking closed surface Gauss's law and the limit of a shrinking closed contour Faraday's law , respectively, which enclose a portion of the material interface.
The simulation to the left shows the induced surface charge density on perfectly conducting metallic objects, while the simulation to the right shows the electric potentials. In the right image, red and blue represent a positive and negative potential, respectively. The top and bottom plates are held at fixed, but different, electric potentials. The middle closed surface has an induced constant floating potential, which, due to symmetry, is the average of the potentials of the plates. The surface charge density is distributed so that each metallic surface is an equipotential surface, an implication of Gauss's law.
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Stock photo. Search Results Results 1 -3 of 3. Theory of Electric Polarization, Vol. Elsevier Science. Used - Good.
Dielectrics and Polarization
Former Library book. Shows some signs of wear, and may have some markings on the inside. Hardcover, Volume 1, second edition, completely revised by O. Van Belle, P. Bordewijk, and A. Rip; surplus library copy with the usual stampings; re ference number removed from spine; light fading, light shelf wear to exteri or; otherwise in good condition with clean text, firm binding.
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