Energy consideration in the two-capacitor problem

Abstract

A derivation of the specific electrostatic energy loss for two interacting capacitors is given. The connecting wires are assumed to be superconducting. The method of derivation is based purely on the Poynting vector involved in the process without any reference to the nature of the mechanism that may be involved in achieving a final equilibrium state.

Energy and Momentum Considerations in an Ideal Solenoid

“…Therefore, regardless of the nature of the mechanism, the amount of the energy loss should always be exactly half the supplied energy of the power supply. It must be emphasized that this energy loss, in all the above cases and possible similar ones, is necessary (or the price that one must pay) to transform the system from an initial non-equilibrium state to a final equilibrium one [23,26]. We must note that our results do not change if one chooses a different function for the current, in which case the reader can easily verify this.…”

“…This other half of the work done finds its way as work done against the induced electromotive force in the windings of the solenoid. This is exactly analogue to the case of charging a capacitor by a power supply, in which it was shown [23] that the stored electric energy in the capacitor comes from the energy carried by the Poynting vector that crosses the plates of the capacitor, and this energy is exactly half the energy delivered by the power supply. While the other half is carried by the Poynting vector that crosses the connecting wires.…”

“…This also happens when a capacitor is charged by a battery, where only half the supplied energy is stored in the capacitor. This pedagogical problem has been a topic of interest by several authors [22][23][24][25][26][27]. When dealing with energy conservation in EM systems, one has to consider all the possible channels through which energy is transported through as the system transforms from an initial non-equilibrium to a final equilibrium state.…”

“…When dealing with energy conservation in EM systems, one has to consider all the possible channels through which energy is transported through as the system transforms from an initial non-equilibrium to a final equilibrium state. For example, it was shown [23] that when charging a capacitor half the work done by the power source is stored in the capacitor while the other half is carried by the Poynting vector which crosses the surface of the connecting wires. The purpose of this paper is to shed some light on the dynamics of the electromagnetic momentum and the energy needed when an electromagnetic system transforms from non-equilibrium to equilibrium states.…”

Entropic considerations in the two-capacitor problem

“…[3,4], the authors focus on energy considerations, while Refs. [5][6][7] discuss specifically the electromagnetic radiation produced by the discharge process. Some of those works neglect the circuit's electrical resistance, but include a self-inductance, while others include both resistance and inductance.…”