Answer:

The presence of matter modifies the ELECTRIC field because

even though the material is usually charge neutral, the field

within the material can cause charge motion, called conduc-

tion, or small charge displacements, called polarization.

Because of the large number of atoms present, 6.02 x 1023 per

gram molecular weight (Avogadro's number), slight

imbalances in the distribution have large effects on the fields

inside and outside the materials. We must then self-

consistently solve for the electric field with its EFFECT on charge

motion and redistribution in materials, with the charges.

resultant effect back as another source of electric field.

3-1 POLARIZATION

In many electrically insulating materials, called dielectrics,

electrons are TIGHTLY bound to the nucleus. They are not

mobile, but if an electric field is applied, the negative cloud of

electrons can be slightly displaced from the positive nucleus,

as illustrated in Figure 3-la. The material is then said to have

an electronic polarization. Orientational polarizability as in

Figure 3-lb occurs in polar molecules that do not share their

No field Electric field E

-0--.

-O- l-q

_E :F =qE

\ d Torque= d x qE

=p x E

F = -qE

p = qd

Electronic polarization Orientation and ionic polarization

(a) (b)

Figure 3-1 An electric dipole consists of two charges of equal magnitude but opposite

sign, separated by a small vector distance d. (a) Electronic polarization arises when the

average motion of the electron cloud about its nucleus is slightly displaced. (b) Orien-

tation polarization arises when an asymmetric polar molecule tends to line up with an

applied electric field. If the spacing d ALSO changes, the molecule has ionic polarization.

electrons symmetrically so that the net positive and negative

charges are separated. An applied electric field then exerts a

torque on the molecule that tends to align it with the field.

The ions in a molecule can also undergo slight relative dis-

placements that gives rise to ionic polarizability.

The slightly separated charges for these cases form electric

dipoles. Dielectric materials have a distribution of such

dipoles. Even though these materials are charge neutral

because each dipole contains an equal amount of positive and

negative charges, a net charge can accumulate in a region if

there is a local imbalance of positive or negative dipole ends.

The net polarization charge in such a region is also a source

of the electric field in addition to any other free charges.

3-1-1 The Electric Dipole

The simplest rpodel of an electric dipole, shown in Figure

3-2a, has a positive and negative charge of equal magnitude q

separated by a small vector displacement d directed from the

negative to positive charge along the z axis. The electric

potential is easily found at any point P as the superposition of

potentials from each point charge alone:

V= q - _ (1)

The general potential and

41reor+

electric

4r8or-

field distribution for any

displacement d can be easily obtained from the geometry

relating the distances r, and r- to the spherical coordinates r

and 0. By symmetry, these distances are independent of the

angle 4. However, in dielectric materials the separation

between charges are of atomic dimensions and so are very

small compared to distances of interest far from the dipole.

So, with r, and r- much greater than the dipole spacing d, we

approximate them as

d

r~r---cos8

2

Then the potential of (1) is approximately

V qdcos0 p-i

41reor 4reor

where the vector p is called the dipole moment and is defined

as

p = qd (coul-m) (4)

The potential at any point P due to the electric dipole is equal to the

sum of potentials of each charge alone. (b) The equi-potential (dashed) and field lines

(solid) for a point electric dipole calibrated for 4vreo/p = 100.

Because the separation of atomic charges is on the order of

1 A(10 10 m) with a charge magnitude equal to an integer

multiple of the electron charge (q = 1.6 X 10-19 coul), it is

convenient to express dipole moments in units of debyes

defined as I debye = 3.33 X 1030 coul-m so that dipole