# Why is the magnetic force not (never) in the opposite direction

In this question I'm talking about the left-handed orientation for the direction of the $x$, $y$ and $z$-axis. This is the coordinate system at the left of the picture below.

I learnt that when you have a moving positive charge with the direction of the velocity $v$ at the positive $x$-axis and a magnetic field $B$ with field lines pointing at the positive y-axis, the particle (charge) experiences a magnetic force directed at the negative $z$-axis.

I was wondering, why is the force in the negative $z$ direction. Why can't it be in the positive $z$ direction?

Edit: I meant a positive charge. :)

Edit 2: Oops, I meant a magnetic force directed at the negative $z$-axis, not the negative y-axis. Why can't it be in the positive $z$ direction?

• Sorry, I meant the negative $z$-axis on a positive charge. I edited my question. Jun 27, 2016 at 13:53
• Well the force cannot be in both positive and negative direction, can it? So either there is no force at all, or there is one with one direction only, and it happens that it is the negative one. What is nice with the law of physics, is that they are obeyed. Jun 27, 2016 at 13:56

The sign of the force direction is just given by convention as $q \vec{v} \times \vec{B}$. Whilst the direction of the force on the particles is clearly something that can be measured, the sign of the charge and the direction of the magnetic field lines are man-made constructs.

For example you would get the same direction for the force if we decided that the magnetic field lines run in the opposite direction and that positive charges are in fact negative.

The whole system is setup to be self-consistent with Maxwell's equations.

However, if you are asking why is there a magnetic force at all, then this is a different question, rooted in the fundamental connection between special relativity and electromagnetism and you will find many answers to such questions on this site already.

• That makes sense. It's a convention, not a physical principle. We can switch the names of positive and negative and switch the direction of the magnetic field 180 degrees and everything still works out. Thanks for you clear answer. I still wonder, what is the fundamental difference between positive and negative charges? What causes the magnetic force to go the other way if you 'change' (theoretically) the charge of a particle from positive to negative (or replace the positive charge with a negative version)? Jun 27, 2016 at 22:49

Well, I think that the magnetic force of the moving positive-charge which you describe is directed at the positive z-axis, if I'm not mistaken ... in other words, all 3 axes come into play when one visualizes which way the magnetic force will point .....

• Sorry, I meant the negative $z$-axis. I edited my question. Jun 27, 2016 at 13:52