This week we are going to explore magnetic force and Ampere's law. The magnetic force acts perpendicular to both the magnetic field and the velocity of a charged particle. It is given by the law:
1.) Find the v x B cross product
For example, if v and B lie in the plane P as shown, in what direction does the force point for a positive charge?
As some of you may have guessed, the force is not necessarily in the direction of the cross product. The charge could be negative.
2) Always check to see whether the charge is positive or negative.
Because the magnetic force is always perpendicular to the velocity, it causes a centripetal acceleration. What effect does a centripetal force have on a particle?
Let's review some basic mechanics. The magnetic force causes an acceleration but does it change the speed of the particle?
What work is done by the magnetic force on a moving charged particle. The work done is the product of the force times the displacement.
What direction relative to the velocity is the displacement dr ? Is it perpendicular or parallel?
The displacement and the velocity are related by
so they must have the same direction. Because the force F is given by the cross product of the velocity with the B field, it must be perpendicular to both. The work is therefore zero.
If no work is done, the kinetic energy cannot change and thus, the speed cannot change.
We are going to investigate the circular motion in more detail in the next section on trajectories.
Go to Trajectories.