North and south of magnetic field

The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule.

Can we determine the north and the south of the magnetic field produced by the current I by using a hand rule?

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Have you tried considering how a small magnetic north pole which doesn't affect the magnetic field would act in this magnetic field? –  Jerry May 8 at 15:24
Sorry, i didn't get you. Are you trying to say that we can determine north and south by using a device? I know that but can we determine it by using a hand rule? –  Rafique May 8 at 15:31
I don't know of any hand rule for this specific purpose. The hand rules I know (Fleming's left hand rule and the Right hand grip rule which relate to magnetic fields) don't give the poles, but the direction of the magnetic field. I guess you'll have to wait for someone else to see your question. –  Jerry May 8 at 15:54
To be honest the same question bugged me too. I think the image of magnetic fields we get in schools is not the best we could get. –  Tomáš Zato May 8 at 22:38

There is no North or South pole in the field around wire. You must understand that the field itself has no poles. Field just consists of force-lines. What we call pole is usually the place when force-lines collide with the physical source of the field (eg. earth, magnet).
But in fact these lines continue even through the source and make elipsoids.

You must imagine this:

And if you take any force-line of the field, you'll be hardly capable to tell, where the north is.

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You're right with the right hand rule. It's accepted because it agreed with the observations. Placing a magnetic needle (compass) in the influence of the (theorized) magnetic field lines, the compass deflects in the direction of the field indicating the curl. The direction how we twist our fingers show the direction of field. Since we've theorized that the lines of force start at the north pole and end at south pole, of course it can be (it already is) determined by the rule...

So, for a curling magnetic field, there's no specific NS poles. It's curled along the direction of lines.

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I always believed that direction of magnetic lines is a pure convention (arbitrary definition). Can we prove (experimentally) that Antarctic is located at the South pole and we, human, chosen a right word (and color) for it? Can we experemantally prove that Antarctic is indeed Antarctic? –  Val May 8 at 18:41
@Val: Yeah. That's what I was talking about. Not only you, but mostly everyone believe it. It's of course an abstract arbitrary definition. Why are you questioning me about the naming? –  Waffle's Crazy Peanut May 8 at 19:16
because you somehow manage to check the definitions experimentally –  Val May 8 at 19:37

The concept of magnetic poles is only defined for localized magnetic systems, which include permanent magnets (or equivalently their surface currents) and induction coils.

The reason for this is that the north/south pole description of a magnet is, mathematically, a description of the magnetic (dipole) moment of the system, where the dipole approximation to the field is only valid "away" from the system. If the wire is infinite, you can't be "far" from it.

For loop, surface, or volume currents, respectively, the magnetic moment is defined as $$\mathbf{m} =\frac{1}{2}\int_C\mathbf{r}\times I\,d\mathbf{l} =\frac{1}{2}\int_S\mathbf{r}\times \mathbf{K}\,dS =\frac{1}{2}\int_V\mathbf{r}\times\mathbf{J}\,dV.$$ If your loop is an infinite wire, the magnetic moment is infinite and its direction depends on where you place your origin. Both of these tell you that this is an incorrect description of your system.

For a simple solenoid, there is a simple rule to get the north and south poles, which is best explained graphically:

Magnetic field lines come out of the north pole, loop around, and go into the south pole (and you can see that there is no analogue of this for a single long wire!).

Also, as far as this is concerned, solenoids and permanent magnets are much the same. This is because the multiple current-carrying coils of the solenoid look very much like the surface spin currents on a permanent magnet, which are the ones that create its magnetic field. (Where they do differ is in the values of the $\mathbf{H}$ field inside the magnet.)

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