THE MAGNETIC FORCE ON A MOVING CHARGE
If a particle with charge q moves with velocity v through a magnetic field B, it will
experience a magnetic force, FB, with magnitude
FB = | q | vB sin θwhere θ is the angle between v and B. From this equation, we can see that if the
charge is at rest, then v = 0 immediately gives us FB = 0—magnetic forces only act
on moving charges. Also, if v is parallel (or antiparallel) to B, then FB = 0 since, in
either of these cases, sin θ= 0. So only charges that cut across the magnetic field
lines will experience a magnetic force. Furthermore, the magnetic force is
maximized when v is perpendicular to B, since if θ = 90°, then sin θ is equal to 1,
its maximum value.
The direction of FB (given by the right-hand rule) is always perpendicular to both v
and B and depends on the sign of the charge q.
Right-Hand Rule:
With your right hand (palm up), point your thumb in the direction of v and your
fingers in the direction of B. If q is positive, FB points out of the palm. If q is
negative, FB points out of the back of the hand.