# Electric field of point charge that has circular motion

We know that moving charge in constant velocity has deformed equation of electric field.

$$E = k \frac{1-\left(\frac{v}{c}\right)^2}{\left[1-\frac{v^2 \sin^2\theta}{c^2}\right]^{3/2}} \frac{q}{R^2}$$

We can derive this equation by put zero vector into acceleration term. But what if the charge has a circular motion? What will the equation be?

• We have MathJax active on the site which means that you can write mathematics that will be neatly typeset in a LaTeX-math-mode-alike language. I'll do this one for you. You should check, BTW, that I've done it right. – dmckee Mar 20 at 1:35
• Do you mean that small charge is moving on a circular orbit much bigger than its size? Then you would get radiation emission. This is a very well-known problem. The relevant search term is 'cyclotron radiation' – Cryo Mar 20 at 2:20
• See en.wikipedia.org/wiki/Synchrotron_radiation. The fields can be derived from the Lienard-Wiechert potentials for a charge in arbitrary motion: en.wikipedia.org/wiki/Liénard–Wiechert_potential – G. Smith Mar 20 at 3:24
• Everybody thanks a lot! I appreciate it! – littlegiant Mar 20 at 6:23
• Are you the inertial or accelerated observer? – Cinaed Simson Mar 20 at 6:59