Question

Using the PhET Radiating Charge applet, explore the difference between "Linear" constant velocity and an accelerating particle. Using Maxwell's equations from the Vacuum and a paragraph or so of your own words, explain why accelerating charges radiate electromagnetic waves while charges at constant velocity don't. You may draw a diagram to support your discussion. [Hint: you don't have to do any real math, just point to features in the equations]

Answer 1

The electric field lines from a point charge evolve in time as the charge moves. Radiation propagate outward at the speed of light as we move up and down the charge.

#Accelerating particle produces transverse fields, while constant velocity produces radial fields.

These are the maxwell’s equations in terms of the electric and magnetic potential.The solution to first equation gives us the formula for electric potential at any given point in space at any give time t. The potential at a point (x,y,z) depends on the charge density at various points in space at an earlier time. What earlier time? The distance between this point and other points divided by the speed of light ‘c’. So the potential at (x,y,z) at time t will depend on the charge density at a point 1 m away but not at its charge density at time t but at time t- 1/c and at a point 2 m away at time t - 2/c and so on. This is called retarded potential because it is retarded in time. If you let ρ go to the limit where it is just defined at one point and write down the time dependence as that of accelerated particle’s ( t2 t2) you will get the sum of two electric fields - one which depends on the velocity and one which depends on the acceleration. The one which depends on velocity is an inverse square field, i.e. it falls off as the square of the inverse of the distance from the charge but the one dependent on acceleration falls off as just the inverse of the distance. Hence this field is more dominant much farther from the charge. This is the radiation field or simply the electromagnetic radiation. It’s frequency varies as the square of the acceleration of the source charge.