Electrical Engineering ⇒ Topic : Uniform Dielectric Medium

Uniform Dielectric Medium

The two parallel plates C and D are separated by a distance d as shown in Figure (a). The relativem permittivity of dielectric between C and D be ε_r. Let a charge +Q coulomb be given to plate C,the flux passing through the medium is:

                                                     figure (a)

                                         ψ = Q coulomb C

Flux density in the medium is:

The electric intensity E is given by

Capacitance of Parallel-Plate Capacitor with Uniform Medium

We have seen that the capacitance of a capacitor can be determined from its electrical properties using the relation C = Q/V. However, it is often desirable to determine the capacitance of a capacitor in terms of its dimensions and relative permittivity of the dielectric. Although there are many forms of capacitors, the most important an-angement is the parallel-plate capacitor.

Consider a parallel plate capacitor consisting of two plates, each of area A square metres and separated by a uniform dielectric of thickness d metres and relative permittivity ε_r, as shown in Figure. Let a p.d. of V 'volts applied between the plates place a charge of +Q and Q on the plates. With reasonable accuracy, it can be assumed that electric field between the plates is uniform

Electric flux density between plates is

                                                       D = Q/A coulomb/m2

Electric intensity between plates is

The ratio Q/V is the capacitance C of the capacitor.

                                       ...in a medium

                                              .......in air

The following points may be noted carefully

(1) Capacitance is directly proportional to  ε_r   and A and inversely proportional to d

(2)   Relative permittivity of medium

(3)  Re-an-anging the relation for C in air

Obviously, permittivity can also be measured in F/m.