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).

This worksheet is the natural sequel of [url=https://www.geogebra.org/m/J9nrrpQH]"Charged particle motion in E + B fields"[/url] and is intended to explore the motion of a charged particle in a [u][i]rotating[/i][/u] electric field ([i]E[/i]) and a perpendicular magnetic field ([i]B[/i]).[br]The main aim of this work is to investigate "[i]the relativity of magnetic and electric fields[/i]", following somehow Richard Feynman' great [url=http://www.feynmanlectures.caltech.edu/II_13.html#Ch13-S6]lecture[/url].[br][br]We can see here that, in some case, the same trajectory can be obtained by a single field ([i]E[/i] or [i]B[/i]) or by a combination of both. [br]The idea of a [i]rotating[/i] 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 [i]electromagnetic[/i] field).[br][br]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.[br][br]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 [i]E[/i] field ([math]\omega_E[/math]) equals the natural angular frequency of the [i]B[/i] field [math]\omega=\frac{Bq}{m}[/math].[br][br]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.[br]Some particular interesting initial conditions can be selected in the yellow drop-down box.[br][br]Further details on the math behind the construction are in the pdf of the previous version (where there was a static [i]E[/i] field and not a rotating one) available [url=https://cdn.geogebra.org/material/m9ygRnR3HXT3jzQBx11JxoOZgX2EkKYU/material-VWeAcxkf.pdf]here[/url]. [br][br]Others, specifically focused on the effects of the rotating [i]E[/i] field, will be added (hopefully) soon, maybe in [url=https://www.lucamoroni.it]www.lucamoroni.it[/url].[br][br]A possible future further step could be to make also the [i]B[/i] field variable in time (i.e. oscillating along the z-axis)