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.