Field lines of two charges.

Field lines of two point charges traced live, their density showing strength, with the neutral point where E = 0.

Set the charges so the neutral point lies one third of the way from q2 to q1 (q1 = 4q2, same sign)

Thinking field lines can cross or are the paths charges follow.

• 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.

Teaching this idea? Put the simulation on your own page or LMS with this code.