General Relations between Fields and Sources

2019 ◽  
pp. 63-84
Author(s):  
Richard Freeman ◽  
James King ◽  
Gregory Lafyatis
Keyword(s):  
Electric Field ◽  
Spatial Variations ◽  
Rate Of Change ◽  
Retarded Time ◽  
Finite Speed ◽  
Radiation Fields ◽  
Source Current ◽  
Field Lines ◽  
General Relations ◽  
Relationship Of

The general relationship of changes in source current, charge and/or position and the fields that they produce are examined in the context of the development of equations that are known as “Jefimenko’s Equations.” These expressions give the fields at a point removed from the source in terms of the charge and current distributions evaluated at the “retarded time.” In this development, the finite speed of light is shown to connect the time rate of change in source conditions to the spatial variations of the potential at the field point. Using a graphical argument, the transverse nature of radiation fields is demonstrated based on electric field lines as envisioned by Faraday.

The electric field of synchrotron radiation

2005 ◽  
Vol 461 (2063) ◽  
pp. 3599-3610 ◽  
Author(s):  
J.H Hannay ◽  
M.R Jeffrey
Keyword(s):  
Synchrotron Radiation ◽  
Electric Field ◽  
Field Evaluation ◽  
Field Pattern ◽  
Relativistic Motion ◽  
Orbit Plane ◽  
Relativistic Limit ◽  
Retarded Time ◽  
Implicit Equation ◽  
Field Lines

A point charge moving uniformly around a circle produces an electric field pattern which co-rotates with it, constituting, for relativistic motion, synchrotron radiation. Surprisingly perhaps, the wealth of knowledge on synchrotron radiation does not seem to include explicit knowledge of the field itself, and of the consequent field lines. As with any relativistic motion, there is an obstruction to writing an explicit formula for the field; evaluation of the retarded time requires solving an implicit equation. However, as the relativistic limit is approached the field grows very strong in a very confined ribbon region shaped like a spiral watch spring. Here, the field can be written as an explicit scaling, or universal similarity, formula, which is our main result. From it the field lines can be derived analytically. In terms of scaled coordinates along the directions of the length, width and thickness of the ribbon, they twist in two side-by-side bundles in ‘bipolar’ cylinder surfaces, mirror symmetric about the orbit plane.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 2: The IGRF

2016 ◽  
Vol 34 (1) ◽  
pp. 67-73 ◽  
Author(s):  
A. D. M. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Field Line ◽  
Electric Fields ◽  
Rate Of Change ◽  
International Geomagnetic Reference Field ◽  
First Order ◽  
Faraday’S Law ◽  
Geomagnetic Fields ◽  
Field Lines

Abstract. A method of mapping electric fields along geomagnetic field lines is applied to the IGRF (International Geomagnetic Reference Field) model. The method involves integrating additional sets of first order differential equations simultaneously with those for tracing a magnetic field line. These provide a measure of the rate of change of the separation of two magnetic field lines separated by an infinitesimal amount. From the results of the integration Faraday's law is used to compute the electric field as a function of position along the field line. Examples of computations from a software package developed to implement the method are presented. This is expected to be of use in conjugate studies of magnetospheric phenomena such as SuperDARN (Super Dual Auroral Radar) observations of convection in conjugate hemispheres, or comparison of satellite electric field observations with fields measured in the ionosphere.

scholarly journals RF-Carpets that Compress Ions to High Density Beams

2015 ◽  
Vol 21 (S4) ◽  
pp. 84-89
Author(s):  
H. Wollnik ◽  
F. Arai ◽  
Y. Ito ◽  
P. Schury ◽  
M. Wada
Keyword(s):  
Phase Space ◽  
Electric Field ◽  
Electric Fields ◽  
Ion Beams ◽  
High Density ◽  
Ion Density ◽  
Field Lines

AbstractIons that are moved by electric fields in gases follow quite exactly the electric field lines since these ions have substantially lost their kinetic energies in collisions with gas atoms or molecules and so carry no momenta. Shaping the electric fields appropriately the phase space such ion beams occupy can be reduced and correspondingly the ion density of beams be increased.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

scholarly journals A Look into Students' Interpretation of Electric Field Lines

2017 ◽  
pp. 342-364
Author(s):  
Esmeralda Campos ◽  
Genaro Zavala
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Random Sample ◽  
Qualitative Approach ◽  
Undergraduate Level ◽  
Field Lines

On Electricity & Magnetism (EM) courses at undergraduate level, the concept of electric field poses one of the most relevant and basic topics, along with the concept of magnetic field. Professors and students may use different diagrams as a tool to visualize the electric field, such as vectors or electric field lines. The present study aims to identify how students interpret and use electric field lines as a tool or resource to describe the electric field. Two versions of a test with open-ended questions were administered in Spanish in a private Mexican university to a random sample of students taking the EM course, and were analyzed with a qualitative approach. It was found that students do not interpret electric field lines diagrams correctly, which may lead to misconceptions. Many students based their answers on the concepts of superposition, force and repulsion.

Sign in / Sign up

Export Citation Format

Share Document