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§ ELECTRIC AND IC FIELDS
Introduction
In ic theory the mks system of units and the Gaussian system of units are the ones most
often encountered. In this section the equations will be given in the mks system of units. If you want the
equations in the Gaussian system of units make the replacements given in the column 3 of Table 1.
Table 1. MKS AND GAUSSIAN UNITS
MKS MKS Replacement GAUSSIAN
symbol units symbol units
E~ (Electric field) volt/m E~ statvolt/cm
~ 2 B~
B (ic field) weber/m c gauss
~ 2 D~ 2
D (Displacement field) coulomb/m 4π statcoulomb/cm
~ cH~
H (Auxiliary ic field) ampere/m 4π oersted
J~ (Current density) ampere/m2 J~ statampere/cm2
~ A~
A (Vector potential) weber/m c gauss-cm
V (Electric potential) volt V statvolt
(Dielectric constant) 4π
4πµ
µ (ic permeability) c2
Electrostatics
A basic problem in electrostatic theory is to determine the force F~ on a charge Q placed a distance r
from another charge q. The solution to this problem is Coulomb’s law
~ 1 qQ b
F = 2 er ()
4π0 r
−12 2 2
where q, Q are measured in coulombs, 0 = × 10 coulomb /N · m is called the permittivity in a
vacuum, r is in meters, [F~ ] has units of Newtons and ber is a unit vector pointing from q to Q if q, Q have
the same sign or pointing from Q to q if q, Q are of opposite sign. The quantity E~ = F/Q~ is called the
electric field produced by the charges. In the special case Q =1,wehaveE~ = F~ and so Q = 1 is called
a test charge. This tells us that the electric field at a point P can be viewed as the force per unit charge
exerted on a test charge Q placed at the point P. The test charge Q is always positive and so is repulsed if
q is positive and attracted if q is negative.
The electric field associated with many charges is obtained by the principal of superposition. For
example, let q1,q2,...,qn denote n-charges having respectively the distances r1,r2,...,rn from a test charge
Q placed at a point P.