Because of the cross product, the magnetic force only involves the component of the velocity that is perpendicular to the magnetic field.
This force causes a centripetal acceleration.
Which v is used in the centripetal acceleration, v, parallel component, or the perpendicular component?
Remember that the centripetal acceleration is a vector that is given by the cross product between the velocity vector and the angular velocity vector, that is, the centripetal acceleration is always perpendicular to both the velocity and angular velocity. For the circular motion shown below show that
The centripetal acceleration also involves the perpendicular component of the velocity:
Thus, the radius of the orbit can be found from the magnetic centripetal force.
There is also a parallel component to the field. What effect will it have on the orbit. In the following animation a particle starts at x = 1, y = 0 with a velocity that has y and z components.
a) If the charge is positive, in what direction does the magnetic field point?
b) How would a positive particle move if the magnetic field is in the opposite direction? Will the trajectory still be helical?
Go to Electrons.