# Why magnetic field lines and force are not orthogonal with magnets?

The below explanation why magnetism exists is superb in this video. The explanation about magnets is also great in this video.

A magnet has atoms with unpaired electrons forming mini magnets. The crystals in the magnet align the atoms in the same direction. If you use a magnet you can align permanently the atoms in some iron ores (e.g. ferrite).

The plane of moving charges inside the magnet has many directions, that are approximately in the plane and perpendicular to the magnetic field lines. The magnet attracts or repels other magnet, with the same type of moving charges.

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1. Imagine a moving charge passing between 2 magnets with speed $\mathbf{v}$ orthogonal to the magnetic field $\mathbf{B}$. This generates a force $\mathbf{F}$ orthogonal to both.

2. Imagine a magnet between 2 magnets. The average moving charges from a central magnet is approximately perpendicular to the line that links the 2 magnets.

Why are the $\mathbf{B}$ magnetic field lines perpendicular to the force $\mathbf{F}$ in situation 1, whereas they both are parallel in situation 2?

I can see a path to a possible answer.

Wikipedia states that

The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles.

a lot of the magnetism in ordinary permanent magnets comes from this intrinsic spin magnetism of the electrons".

Trying to explain spin, Wordpress blog Quantum Moxie comments that

spin isn’t just angular momentum. [...] the total angular momentum of an electron in an atom can be given by the sum of the orbital angular momentum and the spin [...] the rotation of an electron ought to include rotation of its electric field [...] As such, at the most fundamental level, magnetism is a purely relativistic effect. [...] It is not clear that a intrinsic property exists for magnetism (though some have conjectured spin fits the bill, but it depends on how we interpret spin!).

I would be grateful for simple and intuitive explanations that do not depend on formulas.

• In the first case, the force is on an electrically charged particle while it's on a magnetic dipole in the second case. There are no average moving charges in the second case. These are two different types of forces. See (Lorentz force)[en.wikipedia.org/wiki/Magnetic_force] and en.wikipedia.org/wiki/Force_between_magnets Commented Oct 4, 2013 at 11:59
• I've changed the question to deepen in relating to your remarks. Commented Oct 5, 2013 at 3:11

There is a difference between your two cases. When you are talking about a charge passing between magnets you are thinking of it as a uniform magnetic field. But it is not uniform, it gets stronger as you approach the magnets. if it were a uniform field the magnetic dipole you put in the middle would not feel a force along the line of the magnets, although it would still experience a torque.

To see where the force along the magnets comes from, imagine a single charge moving in a circle with velocity always perpendicular to the line of the magnets. If it were a uniform magnetic field the Lorentz force would act perpendicular to the line of the magnets producing an outward radial force. This is what you realized.

But really the field is getting weaker as you go away from the magnets, and since the magnetic field has no divergence that means the field lines must expand outward as you go away from the magnets. You see this on any diagram of the magnetic field of a dipole. So if you look at what the Lorentz force on the charge moving in a circle is now the the magnetic field has a (possibly small) component outwards you will see the charge picks up a force along the line of the magnets (in addition to the original force outward).

I'm thinking a lot about my own question and I guess that I've discerned one possible solution.

Recall that in the imaginary situation there are 2 aligned magnets (SN and NS) and a magnet (SN) between that 2 magnets. The left magnet attract the middle magnet and the right magnet repel the middle magnet.

SN ◄ SN ◄ NS

The magnetism of a magnet results from orbital and rotational spin of unpaired electrons. Each individual movement generates a Magnetic Field B and also has a Force F, related to external magnetic field (from another magnets) and internal magnetic field.

The individual net B acting on a electron and F electron-generated are orthogonal.

There are almost uncountable pair of unpaired electrons in the magnet and the same number of B and F vectors.

There is a external B field acting in the third magnet, however electron movements are also strongly affected by internal magnetic fields from other electrons in the third magnet.

Suppose a X-Y-Z axis system (Z axis from monitor to us), it's a right-hand standard for a negative charge. X is a force, Y is a Magnetic Field and Z is the electron speed with module and direction.

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Suppose two movements M1 and M2 (Speed V1 and V2) with opposite directions in the Z Axis. The positive z movement M1 is related to a Force F1 in X axis and Magnetic Field B1 in Y axis. Suppose that the negative z movement M2 is associated with a Magnetic Field B2 in X axis. In that case, the resulting Force F2 will be in the Y axis!

(In order to imagine this, it's only use to right-hand rule to axis. Turn upside down your middle finger and rotate horizontally: X and Y switch positions)

In that case, the net force and net field magnetic can be in the same direction!

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The spin and angular moment in the electrons, form a very complicated arrangement of movements and magnetic fields, so that above simulated situation is perfectly possible.

Now I know that is not a impossible result. However, there is a additional question:

Why net F strength acting in the third magnet is parallel to net overall B magnetic field?

(source: tutorvista.com)