1.5 EM Properties and Circuit Elements

The electromagnetic properties of rocks are described by three parameters: 1) the electrical conductivity, σ; 2) the electric permittivity, ε; and 3) the magnetic permeability, μ. Each of these is related to the common electrical circuit elements (resistor, capacitor, and inductor, respectively). They are also the proportionality constants that appear in the constitutive relations for the electromagnetic field vectors in Maxwell's equations (Appendix A). They are of fundamental importance in all geoelectromagnetic measurements. First let us relate them to the circuit elements:

Resistor

The current density, J in a resistor is proportional to the electric field, E, i.e.,

J = σE

(1.5.1)

where σ is the electrical conductivity. This relationship is the most general form of Ohm's law.

Capacitor

The current density, J charging a capacitor continues as a field current transversing the dielectric. This field current is equal to the time derivative of the electric displacement, D which is called displacement current density, J _D , i.e.,

J D = (∂D/∂t)

(1.5.2)

where

D = εE.

(1.5.3)

and ε is the electric permittivity.

Inductor

When the current in an inductor changes, and induced voltage, V_L, opposes the change in current, i.e.,

VL = - (∂Φm/ ∂t) .

(1.5.4)

This is the expression of Faraday's law of induction where Φ_m is the magnetic flux,

Φ m = ∫B · ds .

(1.5.5)

The magnetic flux density (or induction), B is given by

B = μH

(1.5.6)

where H is the magnetic field and μ is the magnetic permeability.