Wolfram Alpha:

```Lorentz Force Law
-----------------

In general, the force is defined as the sum of the electric force and
the magnetic force as:

F  = q(E + v x B) where v is the velocity

= q(E + vBsinθ) where θ is the angle between v and B

= q(E + {Fx + Fx + Fx})

= q(E + {(vyBz - vzBy) + (vzBx - vxBz) + (vxBy - vyBx)})

++++++++
----------
+ ^   E Field:
|E  | |F  The direction of the force is parallel to the field
v   v -
----------
--------

N
----------
q.---->v
|B       B Field:
v        The direction of the force is determined by the Right
F        Hand Rule
----------
S

Right Hand Rule
---------------

F
|  /B
| /
|/
q -----v

Thumb in direction of v, fingers in direction of B, palm in direction of F for +ve
charge. Opposite for -ve charge. The RHR is implicit in the component representation
of the cross product.  Thus, for a +ve charge, B in the z direction and v in the x
direction we get:

F = q{(vyBz - vzBy) + (vzBx - vxBz) + (vxBy - vyBx)}

=> Fy = -qvxBz

Which is in accordance with the RHR.
```