electric field

An electric field is the invisible influence a charge spreads through the space around it, ready to push or pull any other charge that comes near. Instead of saying two charges reach across empty space to touch each other, we say the first charge fills space with a field, and the second charge feels the field at its own location. It is the electrical cousin of the gravitational field around a mass.

The electric field E at a point is defined as the force per unit charge that a tiny positive test charge would feel there: E = F / q. Its direction is the direction of the force on a positive charge, and its SI unit is the newton per coulomb (N/C), equivalently the volt per metre (V/m). For a single point charge Q, the field at distance r has magnitude E = k Q / r^2 and points away from Q if Q is positive, toward Q if negative. Once you know E, the force on any charge q placed there is simply F = q E.

The field idea is powerful because it lets you describe what a charge does to space without mentioning any second charge. You can map the field everywhere first, then drop in a charge and instantly know the force. Fields also carry energy and, when they change, can travel as electromagnetic waves, which is what light is. The picture of forces acting through fields, rather than instantly across a gap, runs through all of modern physics.