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Recently I read about the Surface charge density on the current carrying wire. Charges in a wire arrange themselves in such a way that electric field in circuit is constant and to do so positive charges resides near positive plate of capacitor and negative charges resides near negatively charged plate.

Now my question is that the positive charge near the postive plate would increase the potential of positive plate and the negative charges near neagatively charged plate would decrease it's (plate) potential and so the difference of potential between both the plates would also Increase or voltage of capacitor would increase.

But this is clearly violation of conservation of energy law. So how the voltage of capacitor remains constant whereas there is positive charge near positive plate and negative charge near negative plate?enter image description here

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    $\begingroup$ "But this is clearly violation of conservation of energy law. " -> Why? The question is unclear, you may edit it to clarify the point. I suspect that you are forgetting that if you start with a charged capacitor (as in the picture) and you close the circuit, the charge just re-distributes uniformly. $\endgroup$
    – Quillo
    Commented Jul 21, 2023 at 13:22
  • $\begingroup$ Because of increased potential difference between capacitor plates due to surface charge - as potential difference increases potential energy also increases - so from where did this extra energy come $\endgroup$
    – Govind Prajapat
    Commented Jul 22, 2023 at 1:39
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    $\begingroup$ Energy was used to create this initial condition of the system, but this is not a static situation. You start with a lot of potential energy, then the system evolves and this potential energy becomes kinetic energy of the electrons and electromagnetic energy in the electromagnetic field generated by the motion of electrons. Total energy of (the one for electrons plus the one stored in the fields) is conserved. Note that this is exactly point 1 in @JohnDoty nice answer! Ofc some energy also goes into heat (the circuit warms up). $\endgroup$
    – Quillo
    Commented Jul 22, 2023 at 6:39
  • $\begingroup$ Which energy was used to create initial condition ? $\endgroup$
    – Govind Prajapat
    Commented Jul 22, 2023 at 6:40
  • $\begingroup$ Whatever energy you want. This is outside the scope of the problem you describe. What energy is used to charge the battery of your mobile phone? What energy is used to run power plants (wind, fossil, solar, nuclear..)? What energy allowed us to have uranium on Earth, or wind, or chemical energy in the form of fossil fuels? You may go back till the big bang and discover that whatever we can do today is because there was a lot of low entropy energy in the early universe. We use that distributed low-entrppy energy to do things (energy is conserved, but we "ruin it" by increasing entropy). $\endgroup$
    – Quillo
    Commented Jul 22, 2023 at 6:48

1 Answer 1

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You've drawn a closed circuit connecting the plates of a charged capacitor. If you create such a thing, two things happen:

  1. The circuit "rings" as the energy from the capacitor drives a current, which produces a magnetic field around the conductor, which in turn drives a current into the capacitor... The energy thus moves back and forth between the electric field in the capacitor and the magnetic field around the wire.

  2. Resistance in the wire dissipates the energy, heating the wire. This causes the ringing to decay.

There is no violation of energy conservation.

Edit:

Since one really should try to do physics in the real world rather than in abstraction, I did the experiment: I charged up a 4.7 nF capacitor and discharged it through a ~1 meter loop of wire. Here's what happened:

enter image description here

The middle of the screen where it starts to ring is the moment I connected the wire.

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  • $\begingroup$ Are you talking about displacement current?? $\endgroup$
    – Govind Prajapat
    Commented Oct 25, 2022 at 13:30
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    $\begingroup$ @GovindPrajapat The displacement current flows between the capacitor plates. The current in the wire is electrons. They are equal in magnitude. Both contribute to the magnetic field. $\endgroup$
    – John Doty
    Commented Oct 25, 2022 at 14:21
  • $\begingroup$ But that's not my question. I am just asking about the effect of surface charge of wire (as shown in the figure) on capacitor. $\endgroup$
    – Govind Prajapat
    Commented Oct 25, 2022 at 14:49
  • $\begingroup$ @GovindPrajapat I have no idea what you mean. I can tell you what happens and where the energy goes if you connect a wire to a charged capacitor. $\endgroup$
    – John Doty
    Commented Oct 25, 2022 at 15:10
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    $\begingroup$ @GovindPrajapat I show the voltage on the capacitor versus time for the situation in your diagram. $\endgroup$
    – John Doty
    Commented Oct 25, 2022 at 23:55

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