The Electric Field of a Point Charge

Two charges feel a force across empty space with nothing touching them. That is strange enough that physicists split the idea in two: the source charge sets up a field everywhere around it, and any other charge that wanders into that field feels a push or pull from it. This is more than bookkeeping. The field lets you describe the space around a charge completely, before you even decide to put a second charge there. It also sets up the next idea in the unit: potential, which is built from the same field but tracks energy instead of force.

For a point charge q, the field strength at distance r is E = kq/r², where k = 8.99 x 10⁹ N m²/C^2. Double the distance and the field drops to a quarter; triple it and the field drops to a ninth. Direction depends on the sign of the source: a positive charge has a field pointing radially outward, away from itself in every direction, like rays leaving a tiny sun. A negative charge has a field pointing radially inward, toward itself, like rays falling into a drain. Nothing about the field's existence depends on a second charge being present to feel it.

The field equation looks like Coulomb's law with one charge stripped out, and that is exactly what it is: E = F/q_test, the force per unit charge a tiny positive test charge would feel if placed at that point. Strip the test charge out of the formula and the field remains, because it belongs to the source charge, not to whatever you use to probe it. This sets up field superposition next, where fields from multiple sources add as vectors at a point.