# How does the right-hand rule work to find the direction of a moving particle?

i.e. an electron moving eastward along a horizontal line.

Relevance

The Right Hand Rule works to find the direction of the FORCE that acts on a CHARGED PARTICLE moving in an ELECTRIC FIELD. (It works for other things too, but I think that this is the context of your question.)

F = q * v x B

where F, v and B are vectors and q is the (scalar) charge.

The essence is in the "v x B" part -- the cross product of velocity and the field. Suppose that v and B are in the x-y plane. v x B is necessarily perpendicular to the plane. If you have a positive charge, you use the RHR to find out the direction of the force (either up out of the plane or down into the plane) by "curling" the velocity vector toward the field vector. (If you have a negative charge instead, you use a left hand rule or reverse the right hand result.)

If v and B are parallel, then v x B is zero (there is no force). If v and B are perpendicular, then the magnitude of the force is simply

F = q*v*B

where now F, v and B are simply the corresponding magnitudes.

In general, the magnitude can be found with

F = q*v*B*sinΘ

and the direction using the RHR (on a positive charge). Note that when parallel, sinΘ = 0 (zero force), and when perpendicular, sinΘ = 1 and F = qvB as stated above.