How does an accelerating charge distribution generate electromagnetic radiation? The following simplified picture is based on the treatment given in the book by Hecht, "Optics", and looks at an accelerated single charge.
The
diagram below shows a static electric charge (blue), and its associated electric field
lines. These lines extend out to infinity in all directions, and show the direction
of the electric field at any point (not the strength). The red line is drawn to
indicate a particular position in space.
If the charge were a little further to the right than in the first
diagram, you would redraw it easily, as shown alongside. The whole pattern has
merely moved slightly to the right, associated with the new position of the charge.
But what happens if the charge has only just been moved?
The principle of relativity tell us that no information can travel faster than
the speed of light. If the charge started moving from one position to the other a
time t1 ago, people a distance ct1 from the charge
are not able to know that the charge has moved. As far as those further than ct1
away are concerned, the field lines they can measure are associated with the original
charge distribution. Suppose the charge stops moving at a time Dt later. Those within a distance c(t1-Dt) from the charge measure the new set of field lines.
This is shown schematically alongside, at a time t1 after the charge
started moving. The original position of the charge is shown in light blue, and the
moved position is shown as darker blue. Two circles have been drawn. The
larger circle is a distance ct1 from where the charge was.
Outside of this circle the field lines represent the original distribution. The
smaller circle has a radius equivalent to how far light can travel since the charge
stopped moving. Inside this circle, the field distribution is for the moved
charge.
In between the two circles, ie in the part that corresponds to the time when the charge was accelerating, the original filed lines bend to meet up with the new field lines. The exact shape of this part of the field distribution can be determined using relativistic ideas. But even without knowing any of these details, we can reasonably expect the old and new lines to join up. Looking at the diagram, we can see that this means that in between the two imaginary circles there is a region where the field lines are not parallel to lines drawn radially outwards from the charge. In other words, the electric field in between these imaginary circles contains a component that is perpendicular to the direction in which the change in electric field lines is propagating.
Consider the direction shown by the red line. As shown in the diagrams, there is a component of the electric field in the x direction here. When we look at the field associated with a stationary charge, there is no transverse electric field. Suppose the charge moved back again to the left, we would see a transverse component in the opposite direction to that seen above. Thus if the charge oscillated back and fore, we would have an electric field component that likewise oscillated perpendicular to the propagation direction as the "circles" in diagram above expand outwards at the speed of light. While the radial component of the electric field falls off as 1/r2 (Coulomb's Law), the transverse coponent falls off only as 1/r. Thus at large distances the only significant field is the transverse field, often referred to as the radiation field.
This is basically the origin of the transverse electric field associated with light. Associated with the time-varying electric field is a time varying magnetic field, and that is the origin of light! Look at the diagram above, and determine at what angles how much transverse component is seen. What will be the direction and strength of the radiation field at different directions relative to the charge?
We are often interested in the radiation from an oscillating electric dipole. The Albert simulations in the School's PC Classroom allow this to be explored for those who are interested.
Created by, and copyright of, Bruce Sinclair, University of St Andrews; last modified 11/09/01
