1 Preliminary Notions
1.1 The concept of electric charge
Electric charge is defined as the property that characterizes
a particle, or a system of particles, from the point of view of its possible
electromagnetic interaction with other particles, or systems.
Some properties of the electric charge are worth to be
The electric charge of an isolated systems is conserved,
no matter the processes that take place in the system.
Electric charge is quantized, i.e., it is always a multiple
of an elementary charge (the electron charge).
The electric charge does not depend on the motion of the
The most common situation in nature is that of electrically
neutral systems, in which the very large number of positive and negative
charges mutually cancel out.
1.2 The electromagnetic field
The presence of a charge already implies the existence of
an electric field all over the space. This electric field E will
exert a force upon any other charge placed at a given distance of the source
Moreover, if the charge is moving it will also originate
a magnetic field B. This magnetic field shall exert a force upon
any other moving charge at a given distance from the source charge.
When the source charge moves with a nonzero acceleration,
electromagnetic waves are radiated from that charge.
The field obey Maxwell's equations, which are the basis
of Electromagnetic Theory. The force acting upon a charge placed in an
electromagnetic field is given by the Lorentz force:
where v is the velocity of the charge q, and E
and B the electric and magnetic fields.
It should be remarked that electromagnetic interaction
is very strong. For instance, the electric repulsion between two electrons
is about forty orders of magnitude stronger than their gravitational attraction.