Thought experiment (all ideal components): Two 1F capacitors wired in parallel (or ring), with open switches separating them, one cap is uncharged, and the other cap is charged with 1 Coulomb->1Volt->0.5Joules (E=CV^2/2). Then close the switches and let the charge equalize. Calculating the new energy in the system results in E=(1F*0.5V^2/2) * 2caps = 0.25J.
Conservation of energy is not violated though, due to the 0.25J being radiated as an electromagnetic pulse.
This blows my mind. You start with a few first principles: 1)conservation of charge 2)some simple properties of an electric field, electrostatics 3)conservation of energy 4) nothing about magnetic fields 5)calculus 6)anything else implicit? ..... and out of this comes a requirement for the existence of magnetic fields and EM radiation!!!!
I'm an electrical engineer, and have a grasp of Maxwell's equations and EM fields and waves... but I'm missing why this result emerges, nothing I see in the first principles hints at B-fields or EM radiation. Can anyone help? And please, don't start high (from the conclusion) and work down, start from my first principles and work up. Thank you!