Flux and Potential Difference

The concept of flux and potential difference enables a unified approach to be adopted for virtually all the field type of problems. Generally, the flowing quantity is termed the flux and the quantity that drives the flow is called the potential difference. This consistency of method is equally applicable to problems in fluid flow, heat transfer, electrical conduction, electrostatics, and electromagnetism, to name but a few.

In general terms, the flux may be written as

(4.1)

In specific terms, for the flow of an electric current through a conducting medium, equation (4.1) takes the form:

(4.2)

where I = the current in amperes (A)

? = is the conductivity of the medium (siemens/m), i.e., the field characteristic

a = the cross-sectional area of the medium (m ²)

l = the length of the medium (m)

V = the applied potential difference, or voltage (V)

The group ( ?a/ l) is termed the conductance, denoted by G and measured in siemens, thus:

(4.3)

The reciprocal of conductance is referred to as the resistance, R, and is measured in ohms ( ?). Hence,

(4.4)

Equation (4.4) is the familiar Ohm's law, which defines a...