Movement of a Charge in a Magnetic Field
An analysis of the movement of an electric charge in a magnetic field, also discussing the particular case when the charge travels at right angles relative to the field
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Key facts 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: 3), equation (4) becomes: 5) in (6), we get that: