Electric field lines

A field line is a curve whose tangent at every point gives the direction of the net field there; an arrow on it shows which way. Field lines are curves in three dimensions.

The relative closeness of lines shows the relative strength of the field: lines crowd where E is strong and spread out where it is weak. In a uniform field they are equally spaced parallel straight lines.

For a point charge the number of lines through a sphere around it is the same at every radius, while the area grows as r², which is the picture behind E ∝ 1/r². (Solid angle ΔΩ = ΔS/r².)

Lines begin on + charges and finish on − charges; around a lone charge they run out to, or in from, infinity.

In a charge-free region field lines are continuous curves with no breaks.

Two field lines never cross, because at the crossing point the field would have two directions.

Electrostatic field lines never form closed loops, because the electrostatic field is conservative.

Faraday invented the picture and called them lines of force; the number drawn is a choice, only their relative density means anything.