My attention was recently drawn to this video created by Terje Sorgjerd of the Aurora Borealis or the Northern Lights (not to be confused with the Aurora Australis or Southern Lights, of course.)
My own back ground in geophysics has been to specialize in the potential fields of the Earth. These are the heat (steady-state), electrical, magnetic and gravity fields generated by the Earth and which follow a simple equation which we call Laplace's Equation:
∇2φ=0
which simply says that a potential field is one of which the Laplacian in free space is equal to zero. This simply means these fields are always spread out smoothly and continuously, looking like the hillsides in the background of a Teletubbies episode.
There. Now you know as much about geophysics as I do.
And in this video, you can SEE as much geophysics as I do. The aurorae are the effect of ionized particles, blown off by the Sun, delicately impinging on the magnetic field surrounding the Earth. Being electrically charged and moving, they are compelled to line up along the magnetic field lines. Once hooked on these field lines. they are compelled to spin around them. As they move closer in to a magnetic pole of the field, where the magnetic field lines converge, they spin faster and faster, gaining energy, energy which they release as light.
For me, it is exciting to actually SEE these field lines normally invisible to us and to witness them following what the Laplacian describes. Yeah, yeah, yeah, I know I've built a life around believing in the validity of such equations as these anyway but actual seeing that the equations actually WORK is a treat.