The quantity D is the electric displacement vector at the surface and is expressed
in units of C m 2, n is the unit vector normal to the surface, and ps is the surface
charge density and is also expressed in units of C m2. Hence, D-. is the component
of the electric displacement which is normal to the surface.
Dnorm = Ps (3-2)
Note that since the surface is considered a perfect conductor, the electric
displacement inside of the conductor and the tangential component of the electric
displacement along the surface of the conductor are both zero. If the medium above
the plate (air) is linear, isotropic, homogeneous, and non-conducting, then
Dnorm = E,,norm (3-3)
The quantity Enom is the magnitude of the component of the electric field
which is normal to the surface of the plate (expressed in units of V m 1) and e is the
permittivity of the dielectric medium, which is essentially Eo, the permittivity of free
space (8.85 x 10 12 F m 1), for air. Therefore, the expression for ps can be written as
Ps = EoEnorm (3-4)
The total charge on the surface of a conducting plate can be found by integrating
the surface charge density over the area of the plate.
Qplate= PsdA (3-5)
The quantity dA is the differential area on the surface of the plate. If the surface
charge density is uniform (which will be the case if the smallest wavelength comprising
Enorm is much greater than the plate diameter), then the total charge can be found by
multiplying the surface charge density by the area of the plate. The boundary condition
specifies that if the magnitude of the normal component of the electric field is uniform