29:28 – Dielectric Materials

29:28 – DIELECTRIC MATERIALS Dielectric materials, or simple dielectric, are non-conducting materials composed of molecules that either have a permanent dipole moment or molecules that can acquire an induced dipole moment. a) permanent dipole moments The water molecule, H2O is a good example of a molecule having a permanent dipole moment since the electrons from the hydrogen atoms spend more time near the oxygen atom then with the hydrogen atoms. This results in an effective and permanent charge separation. H+ -2 p O H+ b) polarizable materials These are materials composed of molecules that do not have a permanent dipole moment but can acquire one if placed in an electric field. In an atom in the absence of an external electric field, the centers of positive and negative charge overlap, so there is no net dipole moment. + + p = 0 ++ Now, if the atom is placed in an external electric field, say pointing to the right, the center of center of positive charge is displaced slightly to the right and the center of negative charge is displaced slightly to the left, producing a slight charge separation and a resulting induced dipole moment. +++ p + The actual separation between the positive and negative charge is small, on the order of atomic dimensions. However, the net effect of all the dipole moments of all the molecules leads to a macroscopic effect. c) torque on a dipole in an electric field In a sample of water, each hydrogen molecule has a dipole moment, but the dipole moments of each molecule are oriented in random directions. However, as we shall see, when placed in an external electric field, the individual dipole moments tend to align with the field, because the field exerts a torque on them. Consider a simple dipole shown below: E + F+ p F - − The forces F+ and F- produce a torque of magnitude 2F+(d/2) sinθ = qEdsinθ. The vector nature of this torque can be expressed simply as G G G τ = pE× This torque tends to align p along the direction of E. Thus if a sample of dielectric is placed in an G external electric field, the dipoles will all align along the direction of E . d) net effect of placing a dielectric in an electric field E0 E’ The effect of the alignment of the dipoles is to produce a row of positive induced on the right side and a row of negative induced charges on the left side. Within the dielectric, the positive and negative charges effectively cancel each other. The induced charges in the dielectric produce themselves an electric field E’ that partially cancels the external field Eo. The net field within the dielectric is then G GG EE= o + E' This field inside the dielectric is reduced relative to the external field by a factor κ e > 1 called the dielectric constant, so that E E = o κ e For vacuum κe = 1.00000, for air κe = 1.0005, for plastics κe ~ 2 – 3, for glass κe ~ 4 – 5. The very best dielectrics have κe ~ 100 – 300. .

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