Magnetic length of a bar magnet

[phymathlover]

We just started magneto statics in school and were told about the use of magnetic monopoles for problem-solving reasons. So we were told that the magnetic length of a bar magnet differs from its geometrical length. I can't quite seem to figure out why we can't assume the monopoles to be right at the ends of the magnet. I do know that a bar magnet can be compared to a long solenoid but we haven't yet studied about either of them in detail and I suffer epic fails whenever I try to get ahead of the class. So a detailed explanation would be really helpful, thank you!

 

[mfb]

I can't quite seem to figure out why we can't assume the monopoles to be right at the ends of the magnet.

For the field far away from the magnet, you can. You just have to adjust the strength of those virtual monopoles to the distance between them.
For the field close to the magnet, this is not possible, the field is more complicated.

 

[phymathlover]

Could you possibly give me a picture or something of the magnetic fields at the end. So that's the reason then? That the magnetic field lines are complicated? I'm still really confused, a little more detail would be really helpful

 

[mfb]

BBC has a good image http://www.bbc.co.uk/bitesize/ks3/science/energy_electricity_forces/magnets_electric_effects/revision/3/. You don't get that field with two monopoles.

 

[jtbell]

Or see here, which shows the magnetic field lines both outside and inside the magnet:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html