The force acting on a charge traveling at a speed in a magnetic field is given by:
If a charged particle of mass travels with a speed at right angles relative to a magnetic field , then the charge will move in a circle of radius given by:
In order to define the force acting on an electric charge placed in a magnetic field, consider a charge traveling at a speed in a magnetic field . Also, assume that in a time the charge traveled the distance , as highlighted in Figure 1.
We can thus write that:
This force acts in the same direction as that of the lines of force of the magnetic field . If the charge travels at right angles relative to the magnetic field, as for example in Figure 1, then the force will act perpendicular to the direction of the charge's movement, and thus the charge will move in a circle (see Figure 2).
As in this case the force is oriented inwards, it equivalates the centripetal force given by: