7 min readConcept sheet2-mark diagrams and 1-mark questions on the properties of field lines (for example, why two lines never cross)

Electric field lines

Field lines are curves whose tangent at any point gives the field direction. They start on positive charges, end on negative charges, and never cross.

DirectionThe tangent to a field line at any point gives the direction of E there

StrengthLines are close together where E is strong and far apart where E is weak

Start and endLines start on positive charges and end on negative charges (or go to, or come from, infinity)

Uniform fieldParallel, equally spaced straight lines

What field lines show

Faraday pictured the field around charges with field lines. A field line is a curve drawn so that the tangent at every point gives the direction of the field there. The arrow on the line shows which way a positive charge would be pushed. The crowding of lines shows the strength of the field. The number of lines crossing a unit area held at right angles to them is proportional to E. For a point charge, the lines spread over a sphere of area 4πr². So their density falls as 1/r², just like E. The number of lines leaving a charge is taken as proportional to the charge.

Properties of electric field lines

They start on positive charges and end on negative charges. For a single charge, they go to or come from infinity.
In a charge-free region they are continuous, smooth curves with no breaks.
Two field lines never cross. At a crossing, the field would have two directions at one point, which is impossible.
Electrostatic field lines never form closed loops, because the electrostatic field is conservative.
They are close together where the field is strong and spread out where it is weak.
They meet the surface of a conductor at right angles.

How to draw field lines for five standard cases

1
Single positive charge: a dot marked +q with 8 straight lines going radially outward, arrows pointing away.
2
Single negative charge: a dot marked −q with 8 straight lines coming radially inward, arrows pointing towards it.
3
Electric dipole (+q and −q close together): lines leave +q, curve round and enter −q. Draw one straight line along the axis between them. The lines are crowded between the charges.
4
Two equal positive charges: lines leave both charges and bend away from each other. Leave a gap at the midpoint and label it neutral point (E = 0).
5
Uniform field: parallel, equally spaced straight lines with all arrows the same way, as between two oppositely charged parallel plates.

Two rules students mix up

Never crossReason: the tangent at a point gives one direction of E. Two lines crossing would give two directions of E at the same point, which is impossible.

Never form closed loopsReason: the electrostatic field is conservative. A closed field line would mean that the work done round a closed path is not zero, which cannot happen in electrostatics.

Field lines are not the paths of moving charges. A charge released from rest follows a field line only where the line is straight.

In real life

Engineers study field patterns around high-voltage insulators on transmission towers. Where field lines crowd, the field is strong and the air can spark (corona). So the metal fittings near the insulators are made smooth and rounded.

Exam angle

1 marks: “Why do two electric field lines never cross each other?” At the crossing, the tangents would give two directions of E at one point, which is impossible.

2 marks: “Draw the electric field lines for (a) an electric dipole and (b) two equal positive charges close to each other.” (a) Lines leave +q, curve round and enter −q, crowded between the charges. (b) Lines leave both charges and bend away from each other, with a neutral point at the middle.

2 marks: “12 field lines leave charge X; 6 of them end on charge Y and the rest go to infinity. State the signs of X and Y and the ratio of their sizes.” X is positive (lines leave it) and Y is negative (lines end on it). The number of lines is proportional to charge, so |qX| : |qY| = 12 : 6 = 2 : 1.

Remember it

Field lines: out of plus, into minus, never cross, never loop, and crowd where the field is strong.