Derive the electric displacement D in terms of E and P Then

Solution

Consider a parallel-plate capacitor before introducing a dielectric into the space between the plates, the electric field strength is:

E = /₀

where are the surface densities of free charges on the plates and ₀ is the permittivity of free space. Introducing the dielectric causes the field to decrease to the value

E = ( - P)/₀ (1)

reflecting the fact that P coulombs/m2 of the free charges on the plates are now neutralized by the polarization charges on the surface of the dielectric. Rewriting equation (1), we have

= ₀E + P = ₀E + P (2)

The left-hand side of this equation, and consequently the right-hand side as well, depends only on the density of free charges on the capacitor plates. The right-hand side is defined as the electric displacement, D. Thus

D = ₀E + P (3)

Since the value of D depends only upon the density of free charges, it is not altered by the introduction of the dielectric.

An alternative expression to equation (1) for the intensity between the plates of the dielectric-filled capacitor is given by the equation

E = /

Recognizing from equation (2) and (3) that D = , we see that

D = E

Thus, the factor of proportionality relating electric displacement and electric field strength is simply the dielectric constant of the medium.

magnetic field quantity, usually called the \"magnetic field strength\" designated by H. It can be defined by the relationship

H = B0/0= B/0- M

and has the value of unambiguously designating the driving magnetic influence from external currents in a material, independent of the material\'s magnetic response.

The relationship for B can be written in the equivalent form

B = 0(H + M)

H and M will have the same units, amperes/meter. To further distinguish B from H, B is sometimes called the magnetic flux density or the magnetic induction. The quantity M in these relationships is called themagnetizationof the material.

Another commonly used form for the relationship between B and H is

B = mH

where = m= Km0

0 being the magneticpermeabilityof space and

Km therelative permeabilityof the material. If the material does not respond to the external magnetic field by producing any magnetization, then Km= 1. Another commonly used magnetic quantity is the magnetic susceptibility which specifies how much the relative permeability differs from one.