# Lagrangian of moving charge

1. Jun 25, 2015

### Timothy S

If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.

2. Jun 26, 2015

### Alexandre

First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.

3. Jun 26, 2015

### stedwards

A charged pith ball on the edge of a rotating disk, driven at constant angular velocity, would suffice.

4. Jun 26, 2015

### Alexandre

I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out
https://people.ifm.liu.se/irina/teaching/sem4.pdf

5. Jun 30, 2015

### stedwards

For whatever reason, that solution seems to leave out the fields generated by the accelerating charge, though I only scanned the paper. There should be a magnetic field in the far field having an intensity something like $B_z(r,\theta) = (1/r^2 sin \theta) cos(\omega t +f(\rho,t))$, in standard spherical coordinates, accompanied by a perpendicular electric field.

6. Jul 3, 2015

### vanhees71

I'm not sure, what the question is about. If you have given the motion of a charge, maybe you want to know the electromagnetic field due to this moving charge. You find this problem for circular motion in almost any textbook on classical electrodynamics. Look for synchrotron radiation. A good treatment can be found in Landau/Lifshitz vol. II and, of course, Jackson, Classical Electrodynamics.

7. Jul 9, 2015

### Timothy S

Sorry it was a really stupid question on so many levels.