## 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 remarked:

• 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 system.
• 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 charge.

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.