If the space between the plates of a capacitor is filled with an insulator, the capacitance of the capacitor will chance compared to the situation in which there is vacuum between the plates. The change in the capacitance is caused by a change in the electric field between the plates. The electric field between the capacitor plates will induce dipole moments in the material between the plates. These induced dipole moments will reduce the electric field in the region between the plates. A material in which the induced dipole moment is linearly proportional to the applied electric field is called a linear dielectric. In this type of materials the total electric field between the capacitor plates E is related to the electric field Efree that would exist if no dielectric was present:
where [kappa] is called the dielectric constant. Since the final electric field E can never exceed the free electric field Efree, the dielectric constant [kappa] must be larger than 1.
The potential difference across a capacitor is proportional to the electric field between the plates. Since the presence of a dielectric reduces the strength of the electric field, it will also reduce the potential difference between the capacitor plates (if the total charge on the plates is kept constant):
The capacitance C of a system with a dielectric is inversely proportional to the potential difference between the plates, and is related to the capacitance Cfree of a capacitor with no dielectric in the following manner
Since [kappa] is larger than 1, the capacitance of a capacitor can be significantly increased by filling the space between the capacitor plates with a dielectric with a large [kappa].
The electric field between the two capacitor plates is the vector sum of the fields generated by the charges on the capacitor and the field generated by the surface charges on the surface of the dielectric. The electric field generated by the charges on the capacitor plates (charge density of [sigma]free) is given by
Assuming a charge density on the surface of the dielectric equal to [sigma]bound, the field generated by these bound charges is equal to
The electric field between the plates is equal to Efree/[kappa] and thus
Substituting eq.(36) and eq.(37) into eq.(38) gives
or
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