ABSTRACT
The superposition principle requires that an array of charges , which are at distances from a point P, give rise at P to an electric field
1 4
q r E
rπε= ∑ GG
It is common practice to represent electric fields by flux lines which always start at positive charges, terminate at negative charges and never cross, for obvious reasons. The number of lines per unit area gives the strength of an electric field at a given point in space. The analogy with hydrodynamic streamlines is strictly formal, as electrostatics is not associated with flow at all, but illustrates the concept of the continuous distribution of the field which describes the electrostatic interaction. In a similar manner it is often convenient to speak in terms of a continuous charge distribution rather than of arrays of point charges and to introduce a charge density ( ) / Vr dq dρ =G for a volume element or ( ) dSdqr /=Gσ for a surface element. For a continuous charge distribution in a volume V,
the electric field at a point P may be written as an integral
1 V 4P
rE d r ρ
πε= ∫ GG
where the volume element is located at a distance r with respect to the point P. The integration is over the volume occupied by the charge distribution. Electrostatics can be formulated in terms of basic properties of electric fields, as expressed by a flux law and a circulation law, which will be derived from Coulomb's experimental inverse square law (11.1). Let us first calculate the total flux of an electric field over a closed surface S of arbitrary shape which is surrounding a single point charge q (Figure 11.1).
