Field lines never cross

At a point on a field line, what does the arrow show?

Every field drawing in this topic obeys one quiet rule: however tangled the pattern looks, no line ever crosses another.

That rule is physics, not tidiness. The reason sits in what a field line means.

Here is a field drawn correctly: every line runs through the space without meeting another.

A field drawn correctly. Every point sits on at most one line, so every point gets exactly one force direction.

Remember what each line shows: at each point, the direction of the force the field would exert.

Now suppose two field lines crossed at one point.

At the crossing point, the first line would give one force direction. The second line would give a different force direction, at the same point, at the same time.

But the force at a point can act in only one direction at one time.

A crossing would claim two force directions at once. So a crossing is impossible: field lines never cross.

Can two field lines ever cross each other?

Two field lines are drawn heading toward the same point. Can both pass through it?

At one point, the field's force acts in one direction only at one time.

Two lines through one point would claim two force directions at once.

So two lines cannot pass through one point.

No. Field lines never cross.

June says the force at one point in a field can act in only one direction at one time. Is June correct?

Marta says field lines may cross in places where the field is very strong. Is Marta correct?

Your turn

Why do field lines never cross?

In this drawing of the field around a charged sphere, can a line from the top of the pattern ever cross a line from the side?

A field exerts a force on a ball at one point. In how many directions does that force act at one time?