| Electric Displacement Field |
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| CATEGORIES ABOUT ELECTRIC DISPLACEMENT FIELD | |
| electric and magnetic fields in matter | |
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DEFINITION In general, D is defined by the relation : where E is the Electric Field , is the Vacuum Permittivity , and '''P''' is the Polarization Density of the material. If P can be written as a linear function of '''E''', which is the case in most materials, we can write : and by : we arive at the simple formula : where is the Permittivity of the material. In Linear Isotropic media this will be a constant, and in Linear Anisotropic media it will be a rank 2 Tensor (a Matrix ). is called the electric Susceptibility . DISPLACEMENT FIELD IN A CAPACITOR Consider an infinite parallel plate Capacitor placed in space (or in a medium) with no free charges present except on the capacitor. In SI units, the charge density on the plates is equal to the value of the D field between the plates. This follows directly from Gauss's Law , by integrating over a small rectangular box straddling the plate of the capacitor: : The part of the box inside the capacitor plate has no field, so that part of the integral is zero. On the sides of the box, is perpendicular to the field, so that part of the integral is also zero, leaving: |
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