Lorentz Force Equation

The total force on a particle due to electric and magnetic fields is described by the Lorentz force equation:

where q is the charge of the particle, v is it's velocity, and E and B are the external electric and magnetic fields, respectively. In the case where there is only an external electric field, the second term is zero, and the force on the particle of charge q is described by:

This means that a particle with a positive charge will be accelerated along the electric field and a particle with negative charge will be accelerated against the electric field, as shown in the following figure. The magnitude of the force felt by the particle will be proportional to the size of the electric field and the charge on the particle.

The trajectory of a particle can be determined from the force and the velocity of the particle. If the velocity is parallel to the electric field, the particle will follow the field lines. If it is perpendicular to the field, the particle will have a curved trajectory. For example, the particle in the following figure has a velocity of V-zero in the Y direction, perpendicular to the electric field (shown by red lines). The particle follows a parabolic path because it feels a force in the X direction.

In the case where the electric field is zero, the force on the particle will be determined by the particle's charge and velocity as well as the external magnetic field:

The magnetic force on the particle is the cross product of the velocity and the magnetic field. This means that the force is perpendicular to the plane formed by the velocity and magnetic field vectors.

For a more in depth look at what happens to particles in various types of electric and magnetic fields, see the
Particle Motion Module.