# Simple thought experiment -> requirement for EM radiation pops out

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!

• if you conserve energy you might get the new charge to be more on each cap, that may be the correct answer. No radiation I think? Oct 31, 2018 at 1:34
• PhysicsDave, The principle of Charge Conservation is supported without exception by all empirical observations so far. Oct 31, 2018 at 19:38
• Sorry I should have said voltage ... is there a voltage level where charge and energy are conserved .... this may answer the dilemma. Nov 1, 2018 at 1:25
• Dave, the voltage on a capacitor is proportional to charge, please stop throwing out random guesses. Nov 1, 2018 at 21:44
• Ok I was going on intuition, not so random, but I see your point now. If you had 10 or even a hundred caps in parallel the energy does dissipate. The E field gets weaker and weaker as the charge spreads over a larger area. Nov 2, 2018 at 15:35