# Magnetic field of a moving charge: which way to the North pole?

1. Aug 18, 2014

### Jabbu

http://cognizantwire.net/HTMLKHSL/ELECTRON/MAGNETIC/MAGNETIC.HTM

http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_3.html

The first image shows the electron moving in a straight line, and in the second image it's moving in circles. In both images we see the north pole is up and south pole down. But wait a minute. In the first image, what pole is directly in front of us and what pole is on the other side of the electron? What pole is in front and what pole is behind the electron?

So let's go inside the first image and stand on the north pole above the electron. We look down, and see the same thing!? The north pole is again up and the south pole down, huh? It's nowhere and everywhere in the same time, how can this possibly be? Where is that line which usually goes through the both poles and always has a very specific direction, like on the second image? Which way to the north pole?

2. Aug 19, 2014

### Staff: Mentor

In the first picture, the magnetic field lines are identical to the picture below. (Your picture shows magnetic density, not direction)

As you can see, the direction of the poles of the field depend on where you are in relation to the wire/charge. The field lines do not got through the charge at all, which is perfectly okay, as they still form loops. If we bend the wire in a loop, or make the charge move in a loop, we get this next picture. Notice that each slice of the field points in the same direction - into the page on the inside of the loop and out of the page on the outside of the loop. This is where the polarity of the current loop comes from.

3. Aug 19, 2014

### Jabbu

Yes, but does it show S-N direction correctly? If we place a compass below the electron the needle will point the north pole is upwards, and if we place the compass above the electron it will say the same thing. Given the compass is facing us. But turn the compass 180 to face the opposite of us and it will say the north pole is down just where the south pole was a second ago. Two compasses back to back against each other, one points the north is in one direction and the other compass says it's the opposite direction, and as we rotate the compass-pair around the wire this direction rotates along and points to every orthogonal 360 degrees direction around the wire. It's everywhere and yet we can never get there, like chasing Leprechaun at the rainbow's end. Isn't that how it works? Does it make any sense?

Now even less I can see which way to the north pole. Where is it, left, right, up, down, under or above, in front or behind?

4. Aug 19, 2014

### Staff: Mentor

As explained on the text on the page you linked to, next to the picture, the diagram does not show field lines, but rather, lines of constant strength (intensity) of the magnetic field, regardless of the direction of the field.

The magnetic field at any point above the path of the electron (in the plane of the "paper") points perpendicularly into the "paper". Below the path of the electron the field points perpendicularly out of the "paper". The field lines go in circles like they do for a current in a wire. Keep in mind that an electron moving to the right acts like a bit of current I moving to the left, because electrons are negatively charged. Take your second diagram (with the wire) and imagine rotating the wire so it runs horizontally with the current going from right to left.

If you place the compass on the "paper", below the electron, and facing us, the needle's axis of rotation will lie in the same direction as the magnetic field, therefore the needle will not tend to point in any particular direction.

If you hold the compass in front of the "paper", between the electron and yourself, and facing you, then the needle will point upwards, because that is the direction of the field at that point and the needle is free to rotate to that direction.

The needle will point in the same direction as I just described: upwards.

5. Aug 19, 2014

### Orodruin

Staff Emeritus
So what does this tell you about the magnetic field of a moving charge?

6. Aug 19, 2014

### Staff: Mentor

It doesn't show north-south direction at all. It shows the field density of the magnetic field.

No it wont. If the compass is aligned so that we can see the needle, then it won't turn at all because the magnetic field lines are perpendicular to the needle. That is, they run in and out of the page. Above the electron the field lines point towards us, while below they point away from us.

If we place the compass so that the "top" of the compass, the part with the glass that we look through to see the needle, faces the wire, then the needle will align itself with the direction the circular lines are running. I believe the arrows point in the positive direction, so the needle will point with the arrows. Since the field lines run in circles, this means that we can move the compass around the wire and as long as we keep the "top" of the compass facing the wire, the needle will continue to align itself with the field lines.

Note that the poles in a circular loop of wire/current are the result of the field lines running in one direction through the center of the loop. Look at the second picture in my previous post. Each set of circular field lines are just like the ones in the first picture I provided. When you loop the wire, you make it so that the circular field lines all run in the same direction through the center of the loop, and in the opposite direction on the outside of the loop.

7. Aug 19, 2014

### Jabbu

Ok, but there is still no one unique direction that will lead us to the north pole. If we follow the compass we'll end up going in circles. Aren't we supposed to arrive where the magnetic field is the strongest instead of circling around over constant magnetic magnitude?

8. Aug 19, 2014

### Orodruin

Staff Emeritus
If the earth did not physically stop you from doing so, following the magnetic flux lines of the earth would also lead you around in ... well not circles ... but loops. The same thing with a permanent magnet or a coil that you put current through.

9. Aug 19, 2014

### Staff: Mentor

Nope. The reason that the magnetic field is greater near the pole of a magnet is because there are a greater number of field lines per area at the poles.

Note that a magnetic "pole" is a property of a physical magnet. It is not a property of the field. A compass needle will align itself with the direction of the magnetic field lines. When you have current flow through a straight wire, or when you have a moving charge, the magnetic field lines form loops around the wire or the direction the charge is moving. There is no "pole" until you loop the wire or force the charge to move in a circular motion so that the field lines concentrate at the center of the loop.

In a magnet, the field lines loop outwards from the north pole, so a compass needle will point towards the north pole. (Technically that's incorrect, as a compass needle points towards the Earth's north pole, which is magnetically a south pole)

10. Aug 19, 2014

### Staff: Mentor

The magnetic field of an inertially moving classical point charge does not have a north and south pole. Neither does the magnetic field of a straight current carrying wire.

A loop of current has a field with a north and south pole, as does a permanent magnet or an electron, proton, or neutron.

11. Aug 19, 2014

### Jabbu

But they show the top field in blue and the bottom one red. Never mind, it looks like I mixed some angles at the beginning, I was supposed to describe this:

Interesting... who would have thought.

http://www.stmary.ws/highschool/physics/home/notes/electricity/magnetism/intro/barMagnetCompass.jpg [Broken]

If the needle from the top compass de-attached and flew off to stick with the magnet, it would move vertically through the shortest distance right to the middle of the magnet?

If the needle from the compass to the right of the top one de-attached and flew off to stick with the magnet, it would also move vertically through the shortest distance?

Last edited by a moderator: May 6, 2017
12. Aug 19, 2014

### Jabbu

Zeropole, that's even less than a monopole. Isn't that unexpected? The closer we get to the electron the stronger magnetic field becomes. Is there no point where the filed is the strongest and would that not be some kind of pole/dipole type of thing?

13. Aug 19, 2014

### Staff: Mentor

The actual math says $\nabla \cdot B=0$. That is the equation referenced by "no magnetic monopoles" but it does not imply that every magnetic field has a north and a south pole.