9772

The Time-Dependent Electromagnetic Fields of a Relativistic Circular Current

The retarded, time-dependent electromagnetic fields of a relativistic circular current are computed by the Heaviside-Feynman formulas. The radius of the circle of the source is 1 meter and the angular velocity is in radians per second. The charge is represented as a red dot and the constant charge velocity is less than the speed of light.
As you move away from the charge's rotation plane, you can see the retardation effect by observing the discrepancy between the charge's position and the electric field vortex.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

We regard the observation points near the circular source, so that the observation time is equal to the source time and the retardation can be neglected. We see the and component of the electric field in the plane changing with time. When the time is running, in the background you see the current position of the charge in the plane as a red point. The displayed domain of the electric field is 6 meters by 6 meters with 400 vectors. The range goes from -3 meters to +3 meters. A good observation of the source is at with variable . The minimum and maximum values of are 0.1 meter and 2 meters. To observe relativistic effects, set and to their maximum values.
The Heaviside-Feynman formulas are defined in The Feynman Lectures on Physics: Mainly Electromagnetism and Matter, Chapter 21; and Klassische Elektrodynamik, 4. Auflage, Chapter 6.5, by J. D. Jackson.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+