7
Coupling of Electromagnetic Fields into Biological Systems
follows for fields that are tangential (or parallel; labeled t) or normal (or perpendicular;
labeled n) to the interface:
1. The tangential components of electric field strength are continuous across the
boundary (E t1 = E t2 ). Electric fields inside are the same as those outside.
2. The normal components of electric flux densities may differ by an amount equal
to the surface charge density (D n1 − D n2 = ρ). The surface charge on the boundary
is zero for dielectric or nonconducting materials.
3. The tangential components of magnetic field strength may differ by an amount
equal to the surface current density (H t1 − H t2 = J). In all cases, except for perfect
conductors, the surface current density is vanishingly small. Thus, for dielectric
or nonconducting materials, the tangential components of magnetic field strength
are continuous across the boundary (H t1 = H t2 ). The magnetic fields inside are the
same as those outside.
4. The normal components of magnetic flux density are continuous across the
boundary (B n1 = B n2 ). The internal magnetic flux density is the same as the magnetic flux density outside.
However, if the field is neither perpendicular nor parallel to the interface, a combination of the aforementioned boundary conditions prevails. Also, the orientation of the
total electric field at the surface of a boundary separating two media can be derived from
the perpendicular (E n1 ) and parallel (E t1 ) components. The ratio of these components is
equal to the tangent of the angle between them.
tan θ = E n1 /E t1
(1.12)
Thus, the orientation of the total electric field can be determined by knowing its perpendicular (E n1 ) and parallel (E t1 ) components.
1.5 Static Electric and Magnetic Fields
The conservation of charge gives rise to an equation of continuity in the differential
form for current flow such that
·J r
∂ρ( )
r,t
∇ ( )
,t +
= 0
(1.13)
∂t
For static (direct current or zero-frequency) electric fields that do not vary with time and
a semi-infinite dielectric layer, Equation 1.13 reduces to
J n1 = J n2 or σ 1 E n1 = σ 2 E n2
(1.14)
Thus, the current densities across an interface are equal to each other. Maxwell’s
equations (Equations 1.3 and 1.4) in the differential form are given by
∇ · D = ρ
(1.15)
Coupling of Electromagnetic Fields into Biological Systems
follows for fields that are tangential (or parallel; labeled t) or normal (or perpendicular;
labeled n) to the interface:
1. The tangential components of electric field strength are continuous across the
boundary (E t1 = E t2 ). Electric fields inside are the same as those outside.
2. The normal components of electric flux densities may differ by an amount equal
to the surface charge density (D n1 − D n2 = ρ). The surface charge on the boundary
is zero for dielectric or nonconducting materials.
3. The tangential components of magnetic field strength may differ by an amount
equal to the surface current density (H t1 − H t2 = J). In all cases, except for perfect
conductors, the surface current density is vanishingly small. Thus, for dielectric
or nonconducting materials, the tangential components of magnetic field strength
are continuous across the boundary (H t1 = H t2 ). The magnetic fields inside are the
same as those outside.
4. The normal components of magnetic flux density are continuous across the
boundary (B n1 = B n2 ). The internal magnetic flux density is the same as the magnetic flux density outside.
However, if the field is neither perpendicular nor parallel to the interface, a combination of the aforementioned boundary conditions prevails. Also, the orientation of the
total electric field at the surface of a boundary separating two media can be derived from
the perpendicular (E n1 ) and parallel (E t1 ) components. The ratio of these components is
equal to the tangent of the angle between them.
tan θ = E n1 /E t1
(1.12)
Thus, the orientation of the total electric field can be determined by knowing its perpendicular (E n1 ) and parallel (E t1 ) components.
1.5 Static Electric and Magnetic Fields
The conservation of charge gives rise to an equation of continuity in the differential
form for current flow such that
·J r
∂ρ( )
r,t
∇ ( )
,t +
= 0
(1.13)
∂t
For static (direct current or zero-frequency) electric fields that do not vary with time and
a semi-infinite dielectric layer, Equation 1.13 reduces to
J n1 = J n2 or σ 1 E n1 = σ 2 E n2
(1.14)
Thus, the current densities across an interface are equal to each other. Maxwell’s
equations (Equations 1.3 and 1.4) in the differential form are given by
∇ · D = ρ
(1.15)