Page 88 - Maxwell House

68 Chapter 2

solution of Maxwell’s equations how perfect this condition is satisfied on PEC
surfaces, especially around the areas with steep curvature.
2. The surface charge density is equal to normal component of displacement field.

If so, the distribution of free (!) charges on the PEC surfaces immediately follows
from solution of Maxwell’s equations.
3. The normal component of magnetic and inductance fields at the surface of the PEC is
zero. Thus, both magnetic vectors are always tangential to the conductor surface at
each point as shown in Figure 2.3.5. It is worth to check any analytical or numerical
solution of Maxwell’s equations how perfect this condition is satisfied on conductive
surfaces especially around the areas with steep
curvature.
4. The surface current density is equal

to tangential component of magnetic field. If so,
the distribution of this current on the PEC
surfaces immediately follows from solution of
Maxwell’s equations.
5. By definition, the time-independent
magnetic fields are decoupled from electrical
fields (see Table 1.7 in Chapter 1) and
Figure 2.3.5 E-field and D-field independent on material conductivity. It,
components always orthogonal to the therefore, follows that magnetic fields penetrate
PEC surfaces the boundary with PEC with full set boundary
conditions in Table 2.2 and are nonzero inside
PEC. That is why you cannot hide or shield sensitive equipment from the earth
magnetic field inside the Faraday’s cage. It can be done inside superconductors, but it
is too cold there to survive.

2.3.6 Superconductors
The superconductivity is a quite complicated quantum
effect, and although the equivalent conductivity of
superconductor can be considered for time-independent
fields as infinitely large, that is the only part of the story.
In a relatively weak low as -135°C for high-temperature
superconductors), a superconductor drives out nearly all
magnetic field as shown in Figure 2.3.6. It does this by
12
setting up a steady flow of electric currents on its surface
Figure 2.3.6 Superconductor without any E-field in the presence. Experiments
expels nearly all magnetic flux demonstrated that such surface current could remain
practically constant for years. The magnetic field created
by this surface current cancels the magnetic field within the bulk of the superconductor

(medium 2) that is equivalent to [17] 2 = 0 and
= = 0 (2.61)
2
0 2
2
Moreover, on the superconductor surface
1 = 0 (2.62)

12 Public Domain Image, source: http://i.imgur.com/ZbHwxPj.png. Meissner effect [17].