Page 87 - Maxwell House

NEOCLASSICAL THEORY OF INTERACTION 67

of lower dielectric permittivity and reduces the total E-field in the medium 2 of higher dielectric
permittivity. Since the normal component of displacement field is always continuous,
i.e. 1 = across the interface,
2
2
1 = (2.60)
2
1
For example, if 1 = 1 (air) and 2 = 10 (ceramic) the intensity of E-field in the air might
increase 10 (!) times and cause serious problem. Wide variety of solid, liquid and gaseous
dielectric materials ( 2 > 1) is broadly used as insulating material in capacitors, as cooling and
insulating liquid in high voltage power line transformers, as a gaseous medium in electrical
switching equipment preventing corona and electrical breakdown. By accident, in some
circumstances (pure technology, excessive heat, etc.), the tiny air gaps or bubbles ( = 1) are
1
formed inside or on the material surfaces ( 2 > 1). The intrinsic E-field strength increases in
such voids accordingly and can reach the breaking strength (~ 3000 V/mm for dry air at room
temperature, sea level pressure, and normal ionization). It might lead to the disastrous effects
at high level of power like corona or complete electrical breakdown destroying dielectric
material, shutting down separate equipment or the whole system.

Note that the interface, i.e. surface, charges shown in 2.3.4b are not volume charges appeared
in (2.41) and not able to travel freely along the interface. They are bounded by dipoles and
called bound charge. Besides, at the dielectric-dielectric interface a conductivity current ≡
0 because there are no free charges supporting it! Therefore, both tangential components, i.e.
electric and magnetic fields, are always continuous across this kind of interface.
2.3.5 Dielectric-Perfect Electric Conductor (PEC) Interface

We now assume that medium 1 is an ideal dielectric ( = 0) and medium 2 is a PEC ( =
1
2
∞). Recall that there are plenty of free charges in PEC and in presence of external E-field these
charges move to the interface practically momentarily (see 2.3.2) and stay there forming the
surface free charges ≠ 0 defined by (2.46) and surface conduction current ≠ 0 defined
by (2.59). Besides, in any point in medium 2 including interface ≡ 0 at any moment of time.
2
Matching these data with the boundary conditions listed in Table 2.1 we have
Table 2.2

Any time dependence Time-dependent fields Time-independent fields

= = 0 =

= ⁄ = 0 =

2

1
0

1
1 = 0 1 = − 2 =
1

1 = 0 1 = 1 − 1 2 =
0
0
1
1 2
A quick look at Table 2.2 reveals that
1. The tangential vector of electrical and displacement fields at the surface of the PEC is
zero. Thus, both electrical vectors are always orthogonal to the PEC surface at each
point as shown in Figure 2.3.5. It is worth to check any analytical or numerical