The Time-Dependent Electromagnetic Fields of a Relativistic Circular Current

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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.
Contributed by: Franz Krafft (April 2011)
Open content licensed under CC BY-NC-SA
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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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