# North and south poles of a circular magnetic field

1. Aug 9, 2011

### rohitchaky

I have two questions

1. The magnetic field around a straight conductor carrying current forms concentric circles around the magnet. Where are the north and south poles of this magnetic field?

2. Can a permanent magnet be made to generate a magnetic field similar to that of a wire carrying conductor?

2. Aug 20, 2011

### Mbert

To understand this, you first need to ask yourself where are the north and south poles in a current loop (e.g. a ring). If you were to put a compass in this field, what would happen?

M.

3. Aug 20, 2011

### rohitchaky

The compass would point in the direction depending on its location and the direction of current. But as I were to move the compass around the wire in a circular manner, the direction of the north pole will also change. So I never find a unique north pole.

The background for this question is this - I noticed that a current carrying conductor levitates stably over a magnetic field (See attachment). Depending on the direction of current and the magnetic field, the point of levitation is decided. The reason it levitates at that position is because the magnetic field find a position where its magnetic field does not offer opposition to the magnetic field of the permanent magnets. This is summarised in Faraday's laws.

We already know from Earnshaw's theorem that we cannot achieve stable magnetic levitation with static magnetic fields but here it seems like we do achieve such a levitation. So I was wondering if it is possible to generate a circular magnetic field from permanent magnets such that the field is outside the magnet and not inside and in this case where would the north and south poles be.

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4. Aug 20, 2011

### Mbert

Put a paper box over a ring that carries a current such that the magnetic field seen from the outside of the box is the same as a permanent magnet. Now if you move the compass around, what happens? Note that this is the same example, but just to make the notion of north and south poles clearer. It is only a matter of the direction of the field. So for instance, you could "assign" north and south poles location on a solenoid by looking at the direction of the field. Now, for your example, you are talking about a straight wire. Unfortunately, to create a dipole field, you need a current loop. If you understand how it works for the ring, you can stretch this example to get long straight wires, but there will always be a loop (so you always have "north" and "south" poles, depending on how you stretched the ring).

I would say this is because Lorentz' force is equal and opposite to gravity.

I believe such studies have already been performed. Check for instance Maglev and the electromagnetic suspension on Wikipedia. From what I remember, I think that you can achieve static levitation, but it is dynamically very unstable (think for instance if there was a wind gust on the train, or change in the load). However, they can probably get this thing stable (just as B2 aircrafts) by some complex control systems.

M.

5. Aug 20, 2011

### rohitchaky

Yes I did look at maglev and other applications utilizing levitation but these systems are made stable by an external force. The wire is stable without the application of an external force. I am trying to see if a permanent magnet can generate a field similar to the field generated by a straight wire carrying current.

6. Aug 20, 2011

### rohitchaky

A permanent magnet will have a unique north and south pole. Hence my question :) but I guess generating such a field will not be possible. What do you think?

7. Aug 20, 2011

### Mbert

If a permanent magnet has unique north and south poles, what happens when you break this magnet in half? The notion of poles serves the purpose of defining the dipole field. One can think of a permanent magnet as a collection of elementary dipoles (this theory is only to explain the macroscopic behaviour).

I don't know if such a field is possible with permanent magnet. Since the permanent magnet and ring produce similar dipole fields, I suppose that if you stretch the geometry of the ring (to reproduce the behaviour you are looking for) and you stretch the permanent magnet in a similar fashion, the behaviour should be the same?

M.

8. Aug 22, 2011

### rohitchaky

Yes I do know the dipole concept of permanent magnets and the concept of the unpaired electron spin that produces magnetism.

Stretch how? Can you show me a picture?

9. Aug 22, 2011

### Mbert

Well, you could probably create such a field if you use a permanent magnet with the shape of a tube, where the poles are directed in the $\hat{\theta}$ (cylindrical coordinates) direction. To verify if it works, take regular rectangular bar magnets with iron dust and align them to form a circle.

M.