Field lines are a map, not a thing that's really there
Students picture electric and magnetic field lines as physical threads running through space. They're a drawing convention — and confusing the map for the territory causes a specific, predictable set of mistakes.
Field lines are one of the best ideas in physics and one of the most over-read. We draw those neat curves swooping from one charge to another, and students quietly come to believe the lines are there — actual filaments threaded through space, with gaps of nothing in between. From that one misunderstanding, a whole family of wrong answers grows.
The field is everywhere. The lines are just how we chose to draw it.
What the lines actually represent
A field exists at every single point in the region — there are no gaps. To draw that, we'd have to put an arrow at every point, which would be an unreadable mess. So instead we draw a sample: a set of lines that follow the direction of the field, spaced so that where the lines are crowded, the field is strong; where they spread out, it's weak. The density carries the information.
That's the key the over-literal reading misses. The empty space between two field lines isn't empty of field — it just has a field weak enough that we didn't need a line there to show it.
The mistakes the literal reading causes
Once you know the lines are a map, a set of classic errors becomes avoidable:
- "There's no field between the lines." Wrong — the field is continuous everywhere. The lines are samples, not the substance.
- "Field lines can cross." They can't, ever. A crossing would mean the field points two ways at one point, which is impossible — at any point it has one definite direction. If your diagram has an X in it, the diagram is wrong.
- "A stronger source has longer lines." No — it has more densely packed lines. Strength is spacing, not length.
Don't ask how many lines there are; ask how crowded they are. The number is arbitrary — you could draw twice as many. The spacing is the physics.
This is the same discipline as reading a circuit diagram or a free-body diagram: the drawing is a deliberate simplification that keeps the essential thing and throws the rest away. Field lines keep direction and relative strength. Read them for that, and don't ask the picture for information it was never trying to give.