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If we bring a separable dipole (say a single ammonium chloride molecule) from infinity to the center of a capacitor, once the dipole stabilizes and the rotational energy is lost to electromagnetic radiation, the net work done is negative. If the capacitor plates be perforated and the field be strong enough to separate the dipole and the ions pass through without collisions, they then may be accelerated in the same direction by two other capacitors with perforations, in the same direction and then may recombine after exiting because of their electromagnetic attraction. Once they combine, they still have the velocity gained by the two additional capacitors but none of the three capacitors lose their charge. The dipole gains some kinetic energy so where does the energy come from?

The capacitors are not connected to batteries and are pre-charged, the entire setup is in vacuum and gravity is non existent

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they still have the velocity gained by the two additional capacitors but none of the three capacitors lose their charge. The dipole gains some kinetic energy so where does the energy come from?

Although the capacitors have not lost any charge, because of the absence of the charges themselves the field in the capacitor is reduced compared to what it was at the beginning. This reduction in the field leads to a reduced energy density in the field itself.

The reduction in the energy of the field is actually greater than the increase in the kinetic energy. The difference is in the energy of the EM radiation that was produced during the acceleration.

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    $\begingroup$ Thanks for the insight. I figured it out myself and what clicked for me was that after the acceleration, the charges are in a stabler position with regards to the two side capacitors as the negative charge ends up closer to the positive plate and farther from the negative plate than before and vice versa for the positive charge and that release in potential energy appears as the kinetic energy plus some radiation $\endgroup$ Commented Nov 20, 2023 at 15:47

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