Electromagnetics

Electric field

The electric field is the invisible 'force halo' that any charge carries around itself, ready to push or pull on any other charge that wanders nearby. Picture a single positive charge as a tiny porcupine whose quills point straight outward in every direction: those quills are field lines, and a second charge dropped into the picture feels a force along whichever quill it sits on. The field exists whether or not a second charge is present — it is the charge's standing invitation to interact, filling all of space at once.

Quantitatively the field E at a point is the force per unit charge that a tiny test charge would feel there, measured in volts per metre (V/m). Near a charge it is strong; far away it weakens with distance, falling off as 1/r² for a point charge. Inside the dielectric of a capacitor charged to 5 V across a 1 mm gap, the field is a brisk 5,000 V/m — and crank the voltage high enough (about 3 million V/m in dry air) and the field rips electrons free, igniting a spark. Voltage is really just the field added up along a path, which is why a steep field means a big push over a short distance.

E = F / q (units: V/m = N/C)

Field lines never cross (a charge can only feel one net push at a point) and they always start on positive charges and end on negative ones — a picture that makes Gauss's law almost obvious.

Also called
E-fieldE 場