Q & A: Magnetic field lines

Why do magnetic lines of force not cross each other? Why does the direction of the magnetic field change at any point along the magnetic lines of force?
- Anonymous (age 15)
Singapore

It's not really true that magnetic field lines cannot cross, but where they do, the magnetic field strength has to be zero.

Here's why: A magnetic field line is that path in space that points in the direction of the magnetic field at every point along it. Walk along a magnetic field line carrying a compass, and the needle will always point in the direction you need to go in order to stay on that magnetic field line (the needle has to be able to pivot up and down as well as around in a circle like most compasses).

If two field lines crossed, then that is saying that the magnetic field points in two different directions, at one place. There's only one direction to the magnetic field at any place at any time, so this doesn't happen.

Now I said that it could happen if the field is zero -- that's the only kind of magnetic field without a direction. You get this inside of quadrupole magnets, say. Here's how to make such a field. Start with four bar magnets, and arrange them like so:

 

        N

        S

      SN NS

        S

        N

The magnetic field in the center of that thing will be zero, but magnetic field lines will point in towards the center from the left and right, and field lines will point away from the center up and down.

Now you asked about why magnetic field lines bend -- they don't always have to. Some magnets are constructed so the magnetic field lines are as straight as possible (at least over part of their length). Magnetic field lines tend to follow closed loops, though. Ordinary permanent magnets have North and South poles, and the magnetic field lines go out of the magnetic North pole and head towards the South pole, usually curving in the process. Magnetic fields can be produced by electrical currents flowing in wires, and the resulting magnetic field makes loops around the wire. You can arrange a lot of wires so the magnetic field follows a nearly straight path for a while, but eventually the field will bend around as no apparatus is infinitely big.

Tom

(published on 10/22/2007)

magnetic lines of force dos not intersect each other why?
- MANOJ KUMAR KACHHAWA (age 25)
jaipur,rajasthan,india

The magnetic force lines aren't real ingredients of the world but just a way of representing the magnetic field. That field is some vector at each point in space, varying in a continuous way from place to place. The direction of the field line near a point represents the direction of the field. The density of the field lines approximately represents the strength of the field.

Now consider what it would mean if two field lines crossed. At the crossing point, there would be two different directions. But at any point there's only one field direction.

Mike W.

Whoops, I just noticed that Tom had once answered almost the same question, so this is now marked as a follow-up.

(published on 03/04/13)