# Forces on moving charges

I want to know what are the total forces on a moving charge due to another charge.

I heard that moving charges is the cause of all magnetism.So what I think is that if we have a charge in motion relative to another motion the stationary charge (stationary in its own reference frame)acts like a magnet and exerts Lorentz force on other charge. One thing is unclear; does the force on moving charge is magnetic force plus the coulomb force or simply is it that that the total force experienced by moving charge is magnetic only.

I also want to know how can we draw magnetic field lines around stationary charge by using just the fact that another charge is moving. Which side of charge will behave as north pole and which will behave as a south pole?

I am of course considering the possibility to determine the direction of magnetic field without actually doing the experiment and seeing the direction of force which will then give the direction of magnetic field.

• In answer to your first point, you most certainly need to include both he electrostatic and magnetic forces on the charge (although the electrostatic force is taken as negligible in many cases i.e. most ideal MHD calculations) – Zephyr Nov 18 '14 at 9:06
• As for your second point, I think you're a little confused, you can't draw field lines around a stationary charge due to that charge. You can however, draw the field lines of any other moving charge acting on a stationary charge. As for a north pole, the mag field of a moving charge doesn't really look like that, the field lines are loops perpendicular to the path of the particle – Zephyr Nov 18 '14 at 9:09
• If there is only one charge moving, there is no magnetic force since the magnetic field of the moving charge has no effect on a static charge ; and the static charge generates no magnetic field. – TZDZ Nov 18 '14 at 10:35
• It is not exact that moving charges are the cause of magnetism. The electron has an intrinsic magnetic dipole (i.e. even if it is at rest) and UNTIL NOW nobody found inside it some moving charges. I mean, the issue with the electron is still an open question. – Sofia Nov 18 '14 at 23:31

The Lorentz force experienced by a charge $q_1$ is:
$$\mathbf F = q_1(\mathbf E + \mathbf v \times \mathbf B)$$
where x means vector-product. The electric field $\mathbf E$ between charges does not come from magnetic properties of the charges. With the magnetic field the things change. A moving charge $q_2$ produces a current, and a current produces around itself a magnetic field. However, looking from a reference frame in which $q_2$ is at rest, it produces no magnetic field.
You may ask, "then, is there a magnetic force acting on $q_1$"? The answer would be that it depends on the frame of reference. The force is a physical quantity that depends on the frame of reference.