Fundamentals of Electromagnetics - RF/Microwave Interaction with Biological Tissues - page 5

q

E = a r V m

- 1

(1.3)

4 pe r

2

0

Ideally, the electric field is defined in the limit that D q tends to zero. It is a
vector field, radial in the case of a point charge. It comes out of a positive
charge and points toward a negative charge. The lines of electric field are tan-
gential to the electric field in every point. Equation (1.3) is linear with respect
to the charge. Hence, when several charges are present, one may vectorially
add up the electric fields due to each charge, which yields what is often called
the generalized Coulomb's law.
The electric charge may appear in four different forms:

1. It can be punctual, as in Eqn. (1.2). It is then usually denoted q and meas-
ured in coulombs .
2. It can be distributed in space along a line (material of not). It is then
usually denoted r l and measured in coulombs per meter (C m -1 ).
3. It can be distributed in space over a surface (material of not). It is then
usually denoted r s and measured in coulombs per square meter (C m -2 ).
4. It can also be distributed in a volume. It is then usually denoted r and
measured in coulombs per cubic meter (C m -3 ).

When a material is submitted to an applied electric fiel d, it becomes polar-
ized, the amount of which is called the polarization vector . This is due to the
fact that, in many circumstances, electric dipoles are created or transformed
into the material, which corresponds to what is called the dielectric properties
of the material. Hence, the polarization is the electric dipole moment per unit
volume , in coulombs per square meter .
The total electric field in a dielectric material is the sum of the applied elec-
tric field and of an induced electric field, resulting from the polarization of
the material. As a simple example, a perfect electric conductor is defined as an
equipotential material. If the points in the material are at the same electric
potential, then the electric field must be zero and there can be no electric
charges in the material. When a perfect electric conductor is submitted to an
applied field, this applied field exists in all points of the material. To have a van-
ishing total electric field , the material must develop an induced electric field
such that the sum of the applied field and the induced field vanishes in all points
of the material.The induced field is calculated by taking into account the geom-
etry of the problem and the boundary conditions, which can of course be com-
plicated. As another example, a human body placed in an applied electric field
develops an induced electric field such that the sum of the applied field and the
induced field satisfies the boundary conditions at the surface of the body. The
total field in the body is the sum of the applied field and of the induced field.
A new vector field is then defined, known as the displacement flux density
or the electric flux density , in coulombs per square meter similarly to the polar-
ization, defined as

P

D