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Marginal inductance and capacitance of a real wire?

  1. Jan 8, 2016 #1
    Speaking just of long straight wires, not loops, coils or solenoids.

    Ideal wires have no resistance. Of course they would have no capacitance. And real wires have some very small amount of inductance, no?

    Firstly, would an ideal wire have some ideal nonzero inductance? Why/why not? After all, an ideal wire should still setup a circling magnetic field which takes energy, no? Wouldn't that magnetic field around an ideal wire still collapse upon switching the current off to keep a tiny more current going for a little bit longer?

    Secondly, does a real wire, the simplest you could construct, have some tiny degree of capacitance?
  2. jcsd
  3. Jan 8, 2016 #2


    Staff: Mentor

    Are you asking for the answer under circuit theory or under Maxwells equations? They give different answers.
  4. Jan 8, 2016 #3
    I'd be interested in both, but probably more in Maxwell's answer.
  5. Jan 8, 2016 #4


    Staff: Mentor

    So in Maxwells equations an ideal current carrying wire does have a magnetic field and therefore energy is stored in the magnetic field. Inductance isn't a part of Maxwells equations, so about all you can say is that there is a magnetic field and an associated energy density.

    In circuit theory an ideal wire does not have any inductance. A real wire is modeled as an ideal wire plus some other components reflecting the non ideal behavior.
    Last edited: Jan 8, 2016
  6. Jan 8, 2016 #5


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    Oh yes, they would. Everything has a capacitance (relative to the rest of the universe at least). You have a capacitance (about 1nF).
  7. Jan 12, 2016 #6
    IDEAL wires are modeled as having a capacitance?
  8. Jan 12, 2016 #7


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    Gold Member

    Surely, ideal wires are modeled as whatever you choose?
  9. Jan 12, 2016 #8
    Ok I agree, but typically an ideal wire would be modeled as having no capacitance yes? To simplify things.

    I suppose a better question then would be, to consider a very long high voltage low current power line. Would one need to model the capacitance between the terminals of the transmission wire for any practical reason? After all, it's low current, I can't imagine there is a great deal of standing charge separation, though perhaps during the charging up and down phases you'd see some lag between the current and the voltage...?
  10. Jan 12, 2016 #9


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    When we draw black lines to join up our component symbols, the black lines have no resistance, no capacitance, no inductance and, I guess, no length. If these are the ideal wires, then fine. If we are concerned (eg. RF circuits) about the capacitance and inductance we know real wires have, then they have to be shown as additional blocks, or maybe as additional strip lines of given dimensions and properties.
    What puzzled me in your original post was
    This seems to jumble up real & ideal in an odd way.
    I think ideal wires have arbitrary properties that you choose to match your ideal. For me, ideal ideal wires have nothing except electrical connectivity - the black lines on our diagrams.
    But once you start giving them properties such as inductance, then why would you assume the other properties are not there? If a wire has inductance, I think it must have capacitance as well. You might choose to be uninterested in either or both, depending on other factors. Perhaps with high current and low voltage, you might worry more about inductance than capacitance, or at high voltages and low currents, worry more about capacitance than inductance. But there's no "of course" about it.

    I don't know much about power lines, but signal transmission lines (like coax and twin feeders) depend specifically on the ratio between their inductance and capacitance for their main characteristics.

    It depends what you mean by ideal. All real wires have inductance and capacitance.
    But if you say your ideal wire has inductance, you now need to specify its dimensions so that you can calculate it. If you just say, oh this wire has 10nH inductance, you might as well put that as a lumped component and stick to ideal ideal wire.

    And, does a real wire have a tiny bit of capacitance, of course.
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