# Is an electron attracted to one of the magnetic poles in this scenario?

Do magnets attract electrons? I don't think so, but maybe in certain cases they can be? I guess it would depend on what direction the velocity and magnetic field is in so that the force acting on the charge is towards one of the poles but I haven't tried that yet.

If an electron is shot between a north pole and a south pole, is it attracted to any of them? Well the resulting force would either be into or out of the page (right?) so it wouldn't be attracted to any. Can anyone confirm/explain this if I'm wrong?

The magnetic part of Lorentz' force law, which describes the force electric and magnetic fields exert on a point charge, is given by

$$\vec{F}=q\,\dot\;\,\vec{v}\times\vec{B},$$

where $q$ is charge, $\vec{v}$ is the velocity of the moving particle and $\vec{B}$ is the magnetic field. As you can see, the particle has to move in order to be affected by the latter. Furthermore, we can see that the force is given by a cross product between velocity and magnetic field. This means that the resulting force points in a perpendicular direction with respect to the plane spanned by the vectors which are multiplied.

Applying this logic to your example of an electron and two poles, the answer is that it will not be directed towards any of the two, as you have correctly assumed.

The Lorentz force, due to the electron's motion through the field, is always perpendicular to the field direction, and generally won't steer your electron towards or away from either pole.

As Floris points out, the electron also has an magnetic dipole moment. In a nonuniform field, a slowly-moving electron will find its spin aligned or antialigned with the local direction of the field, and will feel a force $F = \mu\nabla B$. However the electron magnetic moment $\mu_e\approx$ 60 $\mu$eV/T is quite small, and for a real electron in a real apparatus subjected to volt-scale stray potentials, a few microelectronvolts of magnetic steering is a negligible correction to the overall motion.

While the dipole-field interaction is usually negligible for the electron, it has been used to build magnetic traps for neutral particles.

Edited to add: if a charged particle (either sign) is steered towards a region of strong magnetic field, such as the field near a magnetic pole or a cusp on a material magnet, the Lorentz force conspires with the rapidly-changing field direction to reflect the particle from the pole.

• +1 for making a start with estimating the magnitude of the force experienced by the magnetic dipole moment (and in the process confirming my hunch that the answer to the question "do magnets attract electrons", is "yes, a little") – Floris Apr 30 '14 at 20:42

Here is an alternative view: I am not sure whether this argument is valid, and hope that comments / voting will help me / us figure this out. I request that people don't downvote because of this qualifying statement - please use comments to contribute to the understanding of this issue.

An electron has a magnetic moment (because of its spin = 1/2). In a diverging magnetic field, a magnetic dipole experiences a net force. From this I conclude that an electron may be attracted to a magnetic pole (since the magnetic field diverges in the vicinity of a pole). This is a different effect than the Lorentz force which relies on the macroscopic velocity of the electron - not its quantum properties.

• You're right! I had more than could fit in a comment, so I added another answer. – rob Apr 29 '14 at 15:17

## protected by Qmechanic♦Aug 8 '15 at 16:08

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