An accelerated charge emits radiation, as taught in our course Electromagnetism and Electrodynamics.

But, how does the electric field of an accelerated charge exactly looks like?

The analytic solution for the electric field in space and time is quite complex. One typically presents approximate solutions close to the charge (near field) and far from the charge (far field). In the Computational Physics course we derive a short numerical scheme, which provides the exact solution for the field in space and time, for any velocity including relativistic.

The first video shows a charge moving in a circle at a speed of 10% of the speed

the light. The solution is similar to the electrostatic solution of a radial field of a charge with a time variable position (the quasi static approximation for the near field).

In the second video the speed of the charge increases to 50% of the speed of light. A tangential field now appears clearly, moving away at the speed of light from the charge. This is the radiation field (approximated by the far field). Note that very close to the charge the field remains quasi static. This radiation is produced in nature by electrons moving in a magnetic field, and is called cyclotron radiation.

In the third video, the speed of the charge increases to 90% of the speed of light. A relativistic effect now leads to radiation emitted into a narrow beam. This is synchrotron radiation, produced by relativistic electrons in a magnetic field. This radiation is produced by a great variety of sources in the Universe.

Thanks to Ayal Beck, a student in the Computational Physics course, for preparing the videos