# Relativity af electric and magnetic fields

- Author:
- Luca Moroni

- 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).

## Charge in a rotating electric field and a (static) magnetic field

## 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 ) equals the natural angular frequency of the .
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

__electric field (__*rotating**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 (*B*field*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)