Field line

A field line is a curve drawn so that its tangent at every point points along the local electric field. Field lines never cross — if they did, the field would have two directions at the crossing point, which is impossible. They begin on positive charges, end on negative charges, and in regions of empty space they simply flow smoothly from one to the other.

Density of field lines encodes the field's strength: where lines are packed close together, the field is strong; where they fan out, it is weak. This is not a convention but a geometric consequence — if you draw lines emanating uniformly from a point charge, the number per unit area falls off as 1/r², matching the 1/r² law of the field itself.

Field lines are a visualisation tool, not a physical object; there is nothing material about them. Their power is in what they let you see at a glance: the dipole's hourglass-shaped pattern, the way lines leave a conductor surface at right angles, the fact that Gaussian surfaces cut through them in predictable numbers. Faraday, who invented them, used the pictures as a way of thinking that eventually became Maxwell's equations.

Michael Faraday drew the first "lines of force" in his notebooks in the 1830s, imagining a physical strand under tension that could store energy and transmit force. Maxwell kept the pictures but replaced the strands with a mathematical vector field; the phrase "field line" stuck.