Electric Flux

Figure 2-2 shows the lines of force resulting from a positive charge q₁. It should be kept in mind that these lines radiate in all directions. The forces in a positive test charge are radially outward. A negative charge produces a field in which the lines of force are exactly the same as in Fig. 2-2, except that the forces are directed radially inward. Thus electrostatic lines of force emanate from positively charged bodies and terminate on negatively charged bodies as shown for the two point charges +q and -q in Fig. 2-3. The field of Fig. 2-3 results from superimposing the radial fields of equal and opposite charges +q and -q.

Figure 2-2. Electric field about a positive charge.

The strength of the electric field due to an isolated point charge varies inversely as the square of the distance from the charge. It is convenient to conceive of the space surrounding the charged body as being permeated by an electric flux emanating from the charged body and equal to the charge on the body. The concept of flux has found applications in other fields. For instance, in the field of illumination the quantity light flux is used. Here the inverse square law also holds because the intensity of illumination varies inversely as the square of the distance from a point source of light. Hence, the amount of flux emanating from a point source and passing through

Figure 2-3. Electric field between equal and opposite charges

a unit area varies inversely as the square of the distance. In fact, if the charge is considered at the center of an imaginary sphere, the flux passing through a unit area of the spherical surface is expressed by

[2-2]

where ψ is the symbol for electric flux and

[2-3]

However, the flux density at any point on the surface of this imaginary sphere is expressed by

[2-4]

in a radial direction as indicated by the unit vector i_r.