Compass and the direction of a magnetic field

[ComptonFett]

According to my physics textbook, one can find out the direction of a magnetic field by a small magnet. The magnet will line itself with the magnetic field with the north pole of the compass pointing in the direction of the field.

http://dl.dropbox.com/u/345710/magnet%26compass.jpg

"Outside" of the magnet this makes sense as the field lines of the compass needle are pointing in the same direction as those of the large magnet. But what happens when the compass needle is on top of the larger magnet and near the north pole (as illustrated in the image by the green dot).

Would the north pole of the compass needle still point in the same direction as the magnetic field of the larger magnet? Or would it point towards the south pole to which it should be attracted? The latter case would make sense because of the attraction between the north & south pole but in this case the magnetic field lines of the compass needle would be in opposite direction to that of the larger magnet (at least at the y-axis of the needle).

 

[technician]

A good way to get to grips with this is to picture a solenoid carrying current producing
a N pole at one end of the solenoid and a S pole at the other.
Outside the solenoid the compass points just like in your diagram.
It is possible to put the compass inside the solenoid and you would find that the lines do go from the S end of the solenoid to the N end inside the solenoid.
It is a bit like current in an electric circuit coming out of the + of a battery and traveling to the - of the battery in the external circuit. But the currenttravels from the - of the battery to the + of the battery inside the battery.

 

[jtbell]

But what happens when the compass needle is on top of the larger magnet and near the north pole (as illustrated in the image by the green dot).

In this case, the compass needle is still outside the magnet.

If you could put the compass inside the magnet and still have it rotate freely, then its north end would point upward, same as inside the solenoid that technician described.

 

[ComptonFett]

In this case, the compass needle is still outside the magnet.

If you could put the compass inside the magnet and still have it rotate freely, then its north end would point upward, same as inside the solenoid that technician described.

You're both right, I should've used solenoid as the system producing the electric field. However, if I was able to put the compass inside the magnet, then its north end would point towards north end of the magnet. This appeared to be counterintuitive in the sense that normally these ends appear to repel each other. Apparently I should't consider the poles ends in the same fashion as static charges which always repel each other. Perhaps I could think that the ends themselves do not repel each other but field lines colliding head-to-head do...

 

[jtbell]

Apparently I should't consider the poles ends in the same fashion as static charges which always repel each other.

Correct. As far as we know, there is no such thing as "magnetic charge." In classical electromagnetism, magnetic fields are always "produced" by electric currents, moving charges, or time-varying electric fields.

We can produce an electric field that is somewhat similar to the magnetic field outside of a solenoid, by taking a cylinder and plastering + and - charge on the two ends. We can study this field using the electrical analogue of a compass needle: a short rod with + and - charges on the ends.

Outside the cylinder, our "electrical compass" behaves very much like a magnetic compass outside a bar magnet or solenoid. Inside the cylinder (assuming it's hollow), on the other hand, the field lines go in the same general direction as the field lines outside (from + to -), so the "electrical compass" points in the opposite direction as the magnetic compass does inside the solenoid.

 

[ComptonFett]

Cheers for the clarification.

 

[DrZoidberg]

In this case, the compass needle is still outside the magnet.

If you could put the compass inside the magnet and still have it rotate freely, then its north end would point upward, same as inside the solenoid that technician described.

Sorry, but that is not correct. The magnetic field of a permanent magnet does indeed behave as if there was "magnetic charge" at it's ends. If you take all the magnetic domains in a magnet and add up their fields the resulting field points from north to south everywhere including the inside of the magnet.
You can also measure the field inside by using the lorentz force. If you shoot an electron through a magnet with a particle accelerator, you will see that the field points from north to south.
You have to distinguish between the real magnetic field and the magnetization of the material. The field produces a lorentz force on a moving charge, the magnetization does not because it is not a real field but a property of the material.
The so called B field inside a ferromagnetic material is actually defined as B = µ0*(H+M). H stands for the real field, M is the magnetization and µ0 the vacuum permeability.
Therefore the B "field" in a magnet has two components. The H field that goes from north to south and is able to deflect electrons. And the "field" due to the magnetization that goes from south to north and can not deflect anything. In the core of a transformer on the other hand and also in an electro magnet H and M point in the same direction.
M and H are mathematically treated as one field because a change in M has the same effect as a change in H on a nearby wire. It induces a current.

http://www.permagsoft.com/english/assets/applets/DemagnetisingCurve.pdf
http://en.wikipedia.org/wiki/Magnetization
http://en.wikipedia.org/wiki/Magnetic_field
http://en.wikipedia.org/wiki/Lorentz_force