Consider the specific example of a positive charge qqq moving in the +x direction with the local magnetic field in the +y direction. In which direction is the magnetic force acting on the particle? Express your answer using unit vectors (e. g., i^i^i_unit- j^j^j_unit). (Recall that i^i^i_unit is written \hat i (or alternatively i_unit can be used.))

The direction of F(B) is in the positive z direction.

Explanation:

The magnetic force acting on a charge particle into a constant magnetic field is given by this equation:

The particle is moving in the positive x direction, it means that the unit vector of the velocity will .

By the other hand, the direction of the magnetic field is in the positive direction of the y axis, so the unit vector of B will be .

As we see, the magnetic force  is given by the cross product between the velocity and the magnetic field, therefore the direction will be the result of the cross product between and . Using the right hand rule we will have:

It means that the direction of F(B) is in the positive z direction.

I hope it helps you!

3. dark matter

empty space could also be a simple vacuum