# Relativity af electric and magnetic fields

Topic:
Circle

## Quick notes 1

Due to the complexity of the calculations it's highly advisable to download the ".ggb" file and run it on a desktop with the classic version of Geogebra (Geogebra5).

## Quick notes 2

This worksheet is the natural sequel of "Charged particle motion in E + B fields" and is intended to explore the motion of a charged particle in a rotating electric field (E) and a perpendicular magnetic field (B). The main aim of this work is to investigate "the relativity of magnetic and electric fields", following somehow Richard Feynman' great lecture. We can see here that, in some case, the same trajectory can be obtained by a single field (E or B) or by a combination of both. The idea of a rotating electric field came to me with the purpose of investigating more closely the possible relationships between the two fields (that are actually different aspects of a single physical entity that is the electromagnetic field). By changing the particle and fields parameters we can get many interesting curves: circles, cycloids, trochoids, parables, cardioids, spirals and other wonderful periodic/quasi-periodic curves. If both fields are present almost all trajectories are bounded, with the exception of the trochoids and the spirals. The latter curves are triggered by a particular "resonance" condition that occurs when the rotation angular frequency of the E field () equals the natural angular frequency of the B field . Three different views are shown in the worksheet: the motion in the xy plane (2D), the motion in 3D and the energy levels against time. Some particular interesting initial conditions can be selected in the yellow drop-down box. Further details on the math behind the construction are in the pdf of the previous version (where there was a static E field and not a rotating one) available here. Others, specifically focused on the effects of the rotating E field, will be added (hopefully) soon, maybe in www.lucamoroni.it. A possible future further step could be to make also the B field variable in time (i.e. oscillating along the z-axis)