Solving Maxwell's Equation for a Toroidal Flux Loop

Craig B. Markwardt

Abstract:

I solve Maxwell's equations in cylindrical coordinates for the case of an initial magnetic flux loop. After solving the partial differential equation, a numerical model is developed which shows the time evolution. I find that the flux loop is not stable, and dissipates as electromagnetic waves at the speed of light. I generated an animated movie which shows this behavior.

(Figure: Density plots showing time evolution of magnetic flux loop)

CLICK HERE FOR MOVIE (magnetic field animated GIF, 400 kilobytes)

ANOTHER MOVIE is HERE (Poynting flux GIF, 110 kilobytes)