• Polarizability Is a Measure of the Ability of a Material to Become

•A dielectric (insulator) is a medium which possess LECTURE 16: DIELECTRIC MATERIALS AND no (or very few) free electrons to provide currents POLARIZABILITY due to an impressed electric field. • Although there is no macroscopic migration of charge when a dielectric is placed in an electric field, microscopic displacements (on the order of the size of atoms or molecules) of charge occur resulting in the appearance of induced electric dipoles.

Dielectric Materials (Cont’d) Polarizability

•A dielectric is said to be polarized when induced • Polarizability is a measure of the ability of electric dipoles are present. a material to become polarized in the • Although all substances are polarizable to some presence of an applied electric field. extent, the effects of polarization become important only for insulating materials. • Polarization occurs in both polar and nonpolar materials. • The presence of induced electric dipoles within the dielectric causes the electric field both inside and outside the material to be modified.

1 Electronic Polarizability Electronic Polarizability (Cont’d) electron cloud nucleus Eapp • In the absence of an • In the presence of an applied electric field, applied electric field, the positively charged the electron cloud is nucleus is surrounded distorted such that it is by a spherical electron displaced in a cloud with equal and direction (w.r.t. the opposite charge. nucleus) opposite to • Outside the atom, the that of the applied electric field is zero. electric field.

Ionic Polarizability Electronic Polarizability (Cont’d) negative positive ion ion − qe qe • The net effect is that • In the absence of an each atom becomes a applied electric field, small charge dipole the ionic molecules are which affects the total randomly oriented p = α e E loc electric field both such that the net inside and outside the dipole moment within dipole material. any small volume is moment polarizability zero. (C-m) (F-m2)

2 Ionic Polarizability (Cont’d) Ionic Polarizability (Cont’d)

Eapp • In the presence of an − qe qe • The net effect is that applied electric field, each ionic molecule is the dipoles tend to a small charge dipole align themselves with which aligns with the the applied electric p = αi E loc applied electric field field. and influences the dipole total electric field both moment polarizability inside and outside the (C-m) (F-m2) material.

Orientational Polarizability Orientational Polarizability (Cont’d)

Eapp • In the absence of an • In the presence of an applied electric field, applied electric field, the polar molecules the dipoles tend to are randomly oriented align themselves with such that the net the applied electric dipole moment within field. any small volume is zero.

3 Orientational Polarizability (Cont’d) Polarization Per Unit Volume

− qe qe • The net effect is that • The total polarization of a given material each polar molecule is may arise from a combination of electronic, a small charge dipole ionic, and orientational polarizability. which aligns with the •The polarization per unit volume is given p = α o E loc applied electric field and influences the by dipole total electric field both moment polarizability inside and outside the loc 2 P = N p = NαT E (C-m) (F-m ) material.

Polarization Per Unit Volume (Cont’d) Polarization Per Unit Volume (Cont’d)

2 • P is the polarization per unit volume. (C/m ) • Eloc is the total electric field that actually • N is the number of dipoles per unit volume. (m-3) exists at each dipole location. • p is the average dipole moment of the dipoles in • For gases Eloc = E where E is the total the medium. (C-m) macroscopic field. • α is the average polarizability of the dipoles in T • For solids −1 the medium. (F-m2)  NαT  E loc = E1−  α = α +α +α   T e i o  3ε0 

4 Polarization Per Unit Volume (Cont’d)

• From the macroscopic point of view, it suffices to use

P = ε 0 χ e E

electron susceptibility (dimensionless)