# Magnetic field cannot accelerate a rest charged particle?

1. Dec 27, 2015

### brian.green

Let's see delocalized electron cloud on a surface of a metal (a piece of iron for example): When a strong Nd magnet get close the spin of these electrons allign to the magnetic field but the electrons don't move. Why? The force is not canceled out. Electrons should move and compressed in one half of the metal, build a charge (density) difference and therefore electric potential difference. It would be EMF and electric current could flow through a wire from one side to another.
In other hand the object get move to the magnet. How can the electrons resist and the whole object cannot? How can the electrons hold their position?

2. Dec 27, 2015

### jambaugh

The force on an individual charged particle due to a B field is proportional to its velocity (v cross B) as well as orthogonal to it. If the particle is not moving then F=0.
(Note that in the relativistic treatment in a frame where the particle IS moving, the transformed EM field has a E component.)

The magnetic force you are imagining is based on the mental picture of a bar magnetic where the N and S poles of the dipole have some separation. They (bar magnets) behave like a balanced pair of monopoles with finite separation and so the closer pole is more strongly attracted than the opposite farther pole is repulsed. However for the electron dipoles there is insufficient separation. A better mental analog for you to use is that the electrons behave like little current loops due to their spin. A magnetic field will induce a net torque on the loop but have no net force on it.

3. Dec 27, 2015

### brian.green

You mean the "spin" get "faster" due to the magnetic force? Or the energy of the magnetic force used up when electrons allign to it? By the way: the magnetic field get weaker while do work on those electrons?

4. Dec 29, 2015

### jambaugh

Not "faster" the spin will change direction but as it is quantized the magnitude remains unchanged. As to the details of the field, weaker or stronger, I am not fully sure (It has been some years since I studied this.) I think the net external field grows stronger or more extensive but much of the behavior is non-intuitive and cannot all be explained in a classical paradigm. (See Bohr-van Leeuwen theorem). I will think about your question further.