the rate of change of the electric field, one or other of the two types of current may dominate the response. Mathematically, the total current consists of two terms; one which depends on the electric field itself and one which depends onthe rate of change of the electric field.

= + (3-2)

= +∈ (3-3)

Quite often it is useful to deal with sinusoidally time varying excitation fields. In this situation, one finds that the dis-placement currents are proportional to the angular frequency.

=( + ∈) (3-4)

where is the angular frequency.

The displacement currents are out of phase with the conductioncurrents by 90° which is what ascribing an imaginary =√( 1) aspect to the displacement component implies. Those familiar with electrical engineering circuitry termi-nology will realize that there is a phase shift between the conduction currents and the displacement currents which indicates that one term is an energy dissipation mechanism and the other one is an energy storage mechanism .A simplified plot of displacement current and conduction currents as well as total current versus frequency is pre-sented in Figure 3-7. Usually there is some frequency above which the displacement currents exceed the conduction currents. In a simple material where the conductivity and the dielectric permittivity are constant, there is a transition frequency, , where the displacement currents and conduction currents are equal. Above this frequency, displace-ment currents dominate; below this frequency, conduction currents dominate. This factor is important when we deal with EM wave propagation. This frequency defines the on set of the low-loss regime important to GPR.

Figure: 3-7 Conduction, displacement and total current versus frequency.

Mathematically the transitionfrequency is defined.