On Energies of Charged Particles with Magnetic Field

The present paper is about magnetic curves of spherical images in Euclidean 3-space. We obtain the Lorentz forces of the spherical images and then we determine if the spherical images have a magnetic curve or not. If a spherical image has a magnetic curve, then after presenting some basic concepts about the energy of a charged particle whose trajectory is that magnetic curve and the kinetic energy of a moving particle whose trajectory is the spherical indicatrix, we find the energy of the charged particle and the kinetic energy of the moving particle.