# Magnetic field lines form loops?

1. Jan 16, 2016

### arul_k

Apart from the orientation of a compass needle and the pattern formed by iron filings, what other proof do we have of magnetic field lines forming loops?

2. Jan 16, 2016

### Incand

Proofs as in experiments? Otherwise it follows from maxwell's law $\nabla\cdot \vec B = 0$ which there been lots of experiments that verify.
The above means pretty much that at every point there is no "net flow". We can also think of it in terms of magnetic flux:
From that equation it follows by the divergence theorem that the flux through any closed surface is zero $\oint_S \mathbf B \cdot d\mathbf a = \int_V (\nabla \cdot \mathbf B) \cdot d\tau = 0$. And since as much leave as enter a surface there is no sources or sinks for the magnetic field lines, i.e. no magnetic monopoles where the field lines can "end up" so they must form closed loops.

Perhaps your question was more/less advanced than this, I only had undergraduate EM so perhaps there's more to it that I'm not aware of.

3. Jan 17, 2016

### arul_k

These equations are derived based on the observation / assumption that magnetic field lines form closed loops and therefore the equations cannot be used as proof of the same.
Of course one could argue that the equations have stood the test of time, and that validates the basic assumption of magnetic field lines forming closed loops.

Has there been any experimental proof?

4. Jan 17, 2016

### Incand

I'm afraid I don't know of any research papers testing this directly but I know there been plenty of research into finding magnetic monopoles and noone have ever been found. But as far as I know there never been any observations of magnetic fields that don't form closed loops which means the theory still holds after over a 100 years. I suspect a lot of our daily technology (transformer for example) use the fact that magnetic field lines close and physicists probably use it in experiments daily. Perhaps someone else can chime in on if there been any more research into this.

Edit: Also the equation stating that the divergence of the magnetic field is zero follow from Biot-Savart law (which is valid for magneto-statics).

5. Jan 17, 2016

### Drakkith

Staff Emeritus
Yes. You already gave two examples in your first post. And if you replace 'compass needle' and 'iron fillings' with 'any device which can detect a magnetic field' then you have even more evidence. Some specific examples would be the behavior of the solar wind as it interacts with Earth's magnetic field and any magnetic confinement device.

6. Jan 17, 2016

### Hornbein

It is a property of the geometry that produces the magnetic field.

http://physics.weber.edu/schroeder/mrr/MRRtalk.html

I'd like to look at the problem more and give a better answer, but I'm busy now. My best guess is that a charge would have a divergent magnetic field if and only if it were measured from the point of view of a charged particle that was moving at the speed of light relative to it. Charged particles have mass, so that can't happen.

7. Jan 18, 2016

### arul_k

Thanks for all the replies. I went thru the link posted by Hornbien and I quote a line from that link:

In summary, we can account for the direction of the magnetic force on the test charge no matter which way it's moving, and this motivates us to introduce a magnetic field vector that points into the page, with the force given by a cross-product of v and B

There dosen't seem to be any reason stated for assuming that the magnetic field vector should point into the page as stated above, so why has this assumption been made.

8. Jan 18, 2016

### Hornbein

The main thing to know is that the magnetic force on a charged particle is perpendicular both to the magnetic field vector and to the velocity vector of the charged particle. The force is never in the direction of the magnetic field vector, like you might expect.

It's so confusing it took science about 50 years to describe it and another 20 years for Albert Einstein to figure out how worked, so don't feel bad if it seems weird.

9. Jan 18, 2016

### Drakkith

Staff Emeritus
It's not an assumption. It's part of the rules of EM theory. The magnetic field vector must point into the page, otherwise the rules of EM theory don't work.

10. Jan 18, 2016

### Staff: Mentor

Yes. The failure to detect magnetic monopoles in all experiments designed to detect them.

This is incorrect. Experiments designed to detect magnetic monopoles assume that Maxwells equations are violated. They then measure the amount of that violation. So far that has always been 0, and if it is ever not 0 it will be huge news and a likely Nobel prize.

11. Jan 19, 2016

### gatopardos

Although if the particle creating the magnetic field is accelerating(i.e. the conductor moving close to c) the magnetic flux lines should be another shape not circular, maybe a pear drop shape.