Chapter 3 : Electric Flux Density, Gauss s Law, and Divergence

Electric flux and electric flux density:
Let us place a test charge at one point in an electric field and allow it to move. The force acting on the test charge will move it along a certain path. This path is called a line of force or a flux line. By placing the test charge at a new location we can create another line of force. Therefore, we can create as many lines of force as we desire by repeating the process. In order not to crowd a region with infinite lines of force, it is customary to arbitrarily state that the number of lines of force due to a charge is equal to the magnitude of the charge in coulombs. The field lines are then said to represent the electric flux. The electric flux lines have no real existence but they are a useful concept in the representation, visualization, and description of electric fields.

Early investigators established the following properties for electric flux:
a) It must be independent of the medium,
b) Its magnitude solely depends upon the charge from which it originates,
c) If a point charge is enclosed in an imaginary sphere of radius R, the
electric flux must pass perpendicularly and uniformly through the surface of the sphere, and
d) The electric flux density, the flux per unit area, is then inversely
proportional to R^2.