Drawing Magnetic Field Lines

Diagrams like the one below are very common, but I would say there are several physics issues with it:

Exactly the sort of field line diagram I don't like

1. The field lines are touching in several places.

Field lines can be defined as showing the direction in which a compass would point if placed at that point. If you draw field lines crossing over, it implies that a compass would simultaneously point in two different directions if you placed it at that point, which is clearly impossible. Field lines that are shown touching are similarly incorrect. This is valuable to mention, even with quite young pupils because a lot of magnetic effects - like repulsion - can be explained in terms of field lines not being able to touch.

 2. The field lines are shown starting and stopping on the surfaces of the magnet.

This suggests that there is no magnetic field inside the magnet, which isn't true, and also that magnetic field lines can start and finish on objects which they can't. Maxwell's Laws include the statement that div B = 0 which states exactly this issue: that North and South poles always exist in pairs and that isolated magnetic poles can't exist. Whilst it's probably folly to think younger pupils should be able to fully appreciate this, it's never too early to steer them away from wrong Physics.

I've often encouraged my pupils to think of them as magnetic field loops rather than magnetic field lines, which might be helpful.