An electron moving along the positive x axis perpendicular to a magnetic field experiences a magnetic direction in the negative y direction. What is the direction of the magnetic field?

Answer 1

F = q V x B, where V and B are vectors and x is the vector cross product. Note that the V comes before the B in the cross product; if it were B x V, the direction would be opposite. In this case, qV is in the -x direction because of the minus sign of q. The force is the -y axis. One assumes that the direction of z is up "out of the page" when looking at the x-y plane.

To have a force F along the -y axis, the B field must be along the -z axis (down). That is because one uses the right hand rule when taking the cross product of qV (along -x) and B (along -z).