How do you define an electric field?

An electric field is a vector field in which an electric charge q point suffers from an electric force F, given by the following equation:

F = qE, where E and F be two vector quantities.

Electric fields come from two sources: electric charges and magnetic fields.

To explain what an electric field we use Coulomb's Law, which expresses the interaction between two electric charges (an equation similar to the law of universal gravitation, but a small scale):

where the first factor used to correct the units to International System and the second r in the equation refers to the unit vector r (unit segment joining q1 and q2).

Well, this is the force that appears when we have two electric charges apart. But more interesting than this is to assume what would be the electric field would be created from a single charge at a given point of space. To do this, we use the expression:

Thus, knowing the field of a charge, we can calculate the force created if we add a load at the point in which we are calculating the field with the equation that we wrote at the beginning of the post.

Needless to say, this field is valid only if we have a single electric charge in space. To calculate the field due to several charges, we calculate all the vectors E, each of the charges and we will add, with the resulting electric field, and if the distribution is continuous (as it is, indeed, any load), we to make use of integrals.