what is lorentz force

The Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. It is the force exerted on a charged particle moving with velocity v through an electric field E and magnetic field B. The entire electromagnetic force F on the charged particle is called the Lorentz force and is given by F = qE + qv × B, where q is the electric charge of the particle. The first term is contributed by the electric field, while the second term is the magnetic force and has a direction perpendicular to both the velocity and the magnetic field. The magnitude of the magnetic force is proportional to q and to the magnitude of the vector cross product v × B. An interesting result of the Lorentz force is the motion of a charged particle in a uniform magnetic field. If v is perpendicular to B, the particle will follow a circular trajectory with a radius of r = mv/qB. If the angle ϕ between v and B is less than 90°, the particle orbit will be a helix with an axis parallel to the field lines. Charged particle accelerators like cyclotrons make use of the fact that particles move in a circular orbit when v and B are at right angles.