# Retarded Fields

When we observe at the night time sky, the star light we see may have begun its journey to earth many years ago. It is conceivable (although unlikely) that a star we are observing no longer even exists. The maximum speed which which information about a physical event is conveyed between two points is the speed of light, c. Imagine an electron that has been moving at a uniform velocity along the x axis for a long time. The electric field is seen to radiate from the instantaneous position of the charge toward infinity. What is observed if the charge suddenly stops at some time, say t=0? The answer depends on the distance from the charge and the time. An observer a distance greater than r = ct away from the charge would not know that charge has stopped and would see the electric field lines radiating from a point ahead of the actually position, i.e., from a point where the charge would have been if it had continued to moved with uniform velocity. An observer closer than r=ct from the charge will see the expected Coulomb field from a stationary point charge. Clearly there must be a discontinuity on the surface r=ct since: (1)the field lines abruptly change direction and (2) the angular distribution of the field for moving charges not uniform but it is uniform for stationary charges.

## Examples

1. Start the charge moving in uniform linear motion with speed of v=0.8c. Wait for the charge to pass the center of the applet twice. On the third pass quickly move the slider to set the speed to 0. Quickly stop the simulation. Notice the information about the change in velocity traveling away from the charge. Follow the field lines outside the "light sphere" toward the x axis and determine where they cross.
2. Dipole radiation results when a charged particle is caused to move sinusoidally. At low speed, i.e., speeds <c, the maximum emission is perpendicular to the direction of oscillation. This radiation pattern changes significantly at high velocities. Observer this transition.
3. Magnetic fields are often used in particle accelerators to store charged particles by bending their trajectories into closed orbits. Unfortunately, this bending produces a centripetal acceleration and therefore radiation. Notice that at low speed the emitted radiation is sinusoidal with a frequency equal to the cyclotron period. At high velocities the the fields tend to bunch into a spiral that produces a broadband pulse once every cyclotron period.