The Electric Field

The region surrounding any object that carries an electric charge is occupied by a field of force known as the electric field. This is evident from the force developed when an exploring particle carrying an electric charge is introduced into such a region. The exploratory charge is also known as a test charge. By convention the test charge is considered positive.

Figure 2-1. Direction of force vector - Coulomb's law

Analyses are made by evaluating effects by means of an imaginary test charge rather than by actually making use of a physical test charge. Thus, in Fig. 2-1 for point charges in free space

q₁ = a charge that produces the field
q_t = test charge that is used to explore the field
r = distance between the charges q₁ and q_t

[2-1]

in any consistent rationalized system of units. If q₁ and q_t are expressed in coulombs, r in meters, and F in newtons, which are the units common to the rationalized MKS system, then ε₀ = 8.854 x 10^-12 farads per m. The factor ε₀ is the dielectric constant of free space. It also represents the capacitance of a meter cube of free space if the electric field intensity is uniform throughout the cube. The vector i_r is a unit vector in the direction along the line connecting the test charge with the source charge.

The charge q₁ produces an electric field of force. The test charge experiences a radial force with q₁ as a center. If the charge q_l is positive, the force on the test charge is one of repulsion.

The forces resulting from the presence of electric charges are extremely powerful and play a vital role in nature. It is the nuclear charge within the atom which distinguishes one element from another and which resists the penetration and disintegration of the nucleus by impinging charged particles. The physical strength and other properties of matter are largely determined by the number and disposition of the electrons swarming about the nuclear charge. Electrostatic forces and principles are used in the experimental procedures of modern physics for deflecting charged particles in motion and for accelerating them to high energies. The characteristics of electrical devices such as vacuum tubes are largely dependent on electrostatic effects. Lightning is a large-scale phenomenon in nature that results from electrostatic forces.