Page 86 - Maxwell House

66 Chapter 2

Here ∆ is the current crossing the loop L in direction of vector � . We denote the density of

this surface current by symbol [A/m] and

− 2 =
1
1 1 � (2.59)
− =
1 2 0
1 2
It is noteworthy to point out that the introduced surface current is exerted by free charges
running along the interface. Table 2.1 is the summary of boundary conditions.
Table 2.1
E-fields Equation Magnetic Fields Equation

1 − = (2.46) = (2.49)

2 − (2.47) = (2.50)
2
1
= ⁄ 1 2

0

3 1 = (2.55) − 2 = (2.59)
2
1

4 1 = 1 (2.55) 1 − 1 = (2.59)
1 2 1 2 0
1 2 1 2
As a final example to illustrate the boundary effects let us investigate several practical cases.
2.3.4 Dielectric-Dielectric Interface
This boundary is shown in Figure 2.3.4 where the interface area A is marked as a straight green
line. We assume that both dielectrics are nonconductive ( = = 0) isotropic and 2 > ,
2
1
1
for a certainty. Using the classical dipole model of dielectric we can expect that the external E-
field exerts forces on existing or induced electric dipoles in both dielectrics aligning them in
0
parallel to as shown in Figure 2.3.4a.
0

a) b)

Figure 2.3.4 a) Dipole model of dielectric-dielectric interface, b) Surface charges and their E-
fields

Taking into account that the higher dielectric constant means a more crowded set of dipoles
there is an excess of positive uncompensated charges at the interface. Thus, the interface will
be charged positively as shown in Figure 2.3.4b creating additional E-field above and below

the interface. Clearly, this extra field makes the total E-field strength greater in the medium 1