Action at a distance is uncomfortable
Coulomb's law works, but it says one charge reaches out and pushes another across empty space with nothing in between. Physicists disliked this 'action at a distance'. Michael Faraday's fix reshaped physics: a charge fills the space around it with an electric field, and that field, right where the second charge sits, is what pushes it. The force becomes local — you feel the field at your own location, not the distant charge directly.
You have met this idea before: mass fills space with a gravitational field, and a nearby mass responds to the local field. The electric field is the same move for charge. It is not just bookkeeping — fields carry energy and momentum, and (once things move) they ripple outward as light. For now, treat the field as the real, physical intermediary of the electric force.
Defining the field: force per unit charge
To measure the field at a point, place a tiny positive test charge q_0 there, measure the force \vec{F} on it, and divide out the charge. The result — force per unit charge — is the electric field \vec{E} at that point. It is a vector, pointing the way a positive charge would be pushed, with units of newtons per coulomb (N/C).
The field is force per unit charge; conversely, a charge q placed in a field E feels a force qE (along E if q>0, opposite if q<0).
The field of a point charge
Combine the definition with Coulomb's law: the force on q_0 from a source q is k\,q q_0/r^2, so dividing by q_0 gives the field of a point charge. It falls off as inverse-square, points radially outward from a positive charge and radially inward toward a negative one.
Magnitude of the electric field a distance r from a point charge q. The direction is radial: away from + charge, toward − charge.
Field lines: making the field visible
Faraday's second great idea was to draw field lines: continuous curves whose tangent at every point gives the field's direction, and whose crowding shows its strength. The rules are simple and worth memorizing: lines start on positive charges and end on negative (or run off to infinity); they never cross (the field has one direction at each point); and where lines bunch closer together the field is stronger.
The picture of a dipole — one positive and one negative charge — is worth studying: lines leave the + charge, curve gracefully through space, and arrive at the − charge. Two like charges instead show lines pushing away from the empty midpoint. These patterns are exactly what determines how a molecule such as water, which is a permanent dipole, responds to nearby charge.
Superposition, and a field to play with
Just as forces added, so do fields. The total field from several charges is the vector sum of each charge's field, computed as if the others were absent — the superposition of fields. This is why field maps of complicated charge arrangements can be built up one charge at a time.