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.



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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.
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