Jerk, curvature and torsion in motion of charged particle under electric and magnetic fields

The existence of the jerk vector and the resulting curvature and torsion are investigated in the motion of a charged particle under the influence uniform of electric and magnetic fields. It is shown that a uniform electric field, by itself,does not produce jerk and hence cannot create torsion. It produces curvature if the initial velocity of the charged particle has a component perpendicular to the electric field. A uniform magnetic field, on the other hand, produces jerk motion, and curvature and torsion of constant magnitudes. The perpendicular and parallel components of the initial velocity of the particle are responsible for the curvature and torsion, respectively. When electric and magnetic fields parallel with one another are present, they both contribute to curvature and torsion. The path is a helix which is continuously being stretched out. As a result, both curvature and torsion approach zero as time progresses.