Understanding Dielectric Polarization: Volume and Surface Charge Densities Explained

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3-7.1 EQUIVALENT CHARGE DISTRIBUTIONS OF POLARIZED DIELECTRICS
To analyze the macroscopic effect of induced dipoles we define a polarization vector, P, as P = lim k=1 Pk Δυ (C/m²), (3-79)
Δυο
)
3-7 Dielectrics in Static Electric Field
1 V = = Par du', 4πεο V ν R2
107
(3-81)
(3-61), respectively, reveals that the electric potential (and therefore the electric field intensity also) due to a polarized dielectric may be calculated from the contributions of is the volume of the polarized dielectric.
The prime sign on a, and V has been dropped for simplicity, since Eqs. (3-88) and (3-89) involve only source coordinates and no confusion will result.
These are referred to as polarization charge densities or bound-charge densities. In other words, a polarized dielectric may be replaced by an equivalent polarization surface charge density pps and an equivalent polarization volume charge density p, for field calculations:
For a surface S bounding a volume V, the net total charge flowing out of V as a result of polarization is obtained by integrating Eq. (3-92). The net charge remaining within the volume V is the negative of this integral:
Q=-Pa
(3-93) mmm
= (-v-P) dv = Sp, dv,
which leads to the expression for the volume charge density in Eq. (3-89). Hence, when the divergence of P does not vanish, the bulk of the polarized dielectric appears to be charged. However, since we started with an electrically neutral dielectric body, the total charge of the body after polarization must remain zero. This can be readily