# Magnetic lines of force

1. Dec 28, 2009

### Lasand

While there is a lot of information on the internet concerning charged particles in a magnetic field, there is very little on the motion of an uncharged ferromagnetic object in the magnetic field of a permanent magnet.

I only found one animation of an uncharged object in the magnetic field of a permanent magnet. It shows the motion of the object to be in parallel with the magnetic lines of force. I observed the motion of a ferromagnetic steel BB to be perpendicular to the magnetic lines of force.

While both objects ended up where the highest flux is, the sleel BB did not take the shortest path, but it's motion seemed to be ruled by being accelerated perpendicular to the lines of force.

http://www.ndt-ed.org/EducationResources/HighSchool/Magnetism/linesofforce.htm

2. Dec 28, 2009

### arunma

That's a good point. They really never teach you about things like calculating the force between two magnets. I guess you could calculate the deflection that one magnet causes on another by using the equation for the torque on a magnetic dipole. But I think there ought to be a net force on the magnet too, and I'm going to have to think for awhile about how to compute that.

3. Dec 28, 2009

### Bob S

When you put a magnetic BB in a magnetic field, you reduce to total stored magnetic energy of the system. The stored magnetic energy is

W = (1/2)∫B·H dVvolume= (1/2μμ0)∫B2 dVvolume

Because B is continuous (Div·B=0), and the relative permeability μ of the BB is much greater than 1, no magnetic energy is stored in it (or in its dipole field).

Now recall that the force in the z direction is Fz= ∂W/∂z

So the magnetic BB is pulled into regions of higher B.
Bob S

4. Dec 29, 2009

### Lasand

Hello arunma;

I've played with compass needles a lot and observed them line up in parallel with the magnetic lines of force. We've seen pictures of iron filings in magnetic fields and how they concentrate where the flux is the densest, but in a short period of time the situation is no longer dynamic as far as motion of the iron filings is concerned. It was the path of motion of the steel BB that caught my interest.

5. Dec 29, 2009

### Bob S

Static magnetic fields do work on the BB by using the change in stored potential energy in the magnetic field to produce kinetic energy.
Bob S

6. Dec 29, 2009

### Lasand

Hello Bob S;

When the steel BB is pulled into regions of higher B, it is the path the BB took that caught my interest. If the geometry of the field lines is curved, then the path of the BB seems to be curved. A small magnet might not show it, but since the cow magnet is 3 inches long you can see that the path can be sort of straight to the body of the cow magnet, then goes to the place of highest flux from there. This is not a straight path, but it seems to be perpendicular to the geometry of the lines of force in both segments of the path.

In the clip where I have the magnets N pole toward the other magnet's S pole, I place the BB where it can accelerate toward higher flux. There is a momentum overshoot then oscillation till the BB comes to rest in the center of densest flux.

Are we in agreement that the path the BB takes is perpendicular to the magnetic lines of force? Pulled into regions of higher B is not specific as to whether the steel BB would have motion in parallel with the lines of force, or perpendicular to the lines of force.

7. Dec 29, 2009

### Lasand

If there is a rule that ferromagnetic material be accelerated orthogonal to the magnetic lines of force, then wouldn't a spacecraft with ferromagnetic material onboard gain acceleration during a particular trajectory flyby above what is predicted by gravitation alone?

8. Dec 29, 2009

### Bob S

Momentum of the BB is conserved along orthogonal directions in space, but the magnetic field lines curve. This can lead to overshoot. The acceleration of the BB is along the magnetic lines of force, but the velocity of the BB has no such constraint.
Bob S

9. Dec 29, 2009

### marcusl

A spherical steel BB will have a dipole moment induced in it by the magnetic field. The force, hence acceleration, of a dipole in a field is
$$\vec{F}=(\vec{m}\cdot\vec{\nabla})\vec{B}$$
so that it is along the gradient of the B field. This need be neither perpendicular nor parallel to the field lines themselves.

10. Dec 29, 2009

### Bob S

The x, y, and z component of the force on the BB are

Fx = ∂W/∂x
Fy = ∂W/∂y
Fz = ∂W/∂z

where W is the total stored magnetic energy in the system.

The resultant force on the BB is the vector sum of these, which is equal to W

Bob S

11. Dec 30, 2009

### Lasand

Thank you for your replies.

12. Dec 30, 2009

### Lasand

Hello marcusl;

I placed a cheap compass on the surface of water. The needle was pointing toward magnetic north. I moved a permanent magnet toward the container and the magnetic dipole of the compass needle felt torque and lined up in parallel with the magnetic lines of force, however the ferromagnetic mass of the needle went into motion more or less perpendicular to the lines.

13. Dec 31, 2009

### marcusl

Hi Lasand,

That's a nice experiment that you performed. There's no contradiction. Note I said that force doesn't have to be at any particular angle to the field lines. The force is instead along the field gradient (that is, the direction where the field lines become more densely packed), which is what you observed.

In the experiment you video taped, your magnet is magnetized along its axis. For the geometry you chose (compass located on a line normal to the magnet axis), the gradient is normal to the field lines and so is the force. If you repeat the experiment with your magnet turned 90 degrees so the compass is located on a line along the magnet axis, the compass should now move along the axis of your magnet, that is, along the field lines.

Perpendicular to field lines in one case, parallel in the other. It is not the field that matters but the field gradient.

Last edited: Dec 31, 2009
14. Dec 31, 2009

### Lasand

Hello marcusl;

The surface of the water was not flat, so I could not do a real good experiment. Some day I might get a bigger container where the water might be more level in the center. The field lines also had too much curvature. I could rig up two cow magnets to get a 6 inch length instead of the single 3 inch length. But it is kind of a pain doing this as my camcorder is Hi-8 analog and it takes time to convert to digital to get in the computer then upload to youtube.

15. Jan 1, 2010

### Lasand

Last edited by a moderator: Sep 25, 2014
16. Jan 2, 2010

### Born2bwire

Make of what? I do not see what it is you are referring to.

17. Jan 3, 2010

### Lasand

First I placed the magnets with opposite poles facing each other. I expected to see the ferromagnetic steel BB rapidly oscillate like a pendulum when suspended between the poles. This sort of happened, but wasn't good enough for a video clip.

I then placed the magnets with like poles facing each other. This changed the field curvature configuration. I found it interesting that the much more massive uncharged BB seemed to be trying to spiral down the magnetic lines of force like an electron. I am sure this isn't the case and that it is just a rotary oscillation.

I don't understand some of the things Tesla did. One drawing showed a capacitor that could be adjusted in order to be close to a coil. Tesla seemed to be fascinated with both mechanical and electrical resonance.