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Correctness of the quasistatic EMFT approximation

  1. Jan 9, 2016 #1
    Hello! I'm just trying to make sure I understand Maxwell, Biot-Savart, Faraday, etc well enough. What I'm wondering about is when the quasistatic treatment is indeed approximate, and when it is, assuming an equal if time-varying current, correct.

    Suppose, first, that we have a steadily increasing current I(t) - that is, dI/dt = k, some constant. The wire (or solenoid, or whatever) is short enough that the current is equal everywhere. We compute the magentic field from Biot-Savart, find the change over time in flux, and thus obtain the induced emf by Faraday's law of induction. As I understand the textbook explanation, this is only approximate (however close), because Biot-Savart only applies for steady current. But any error, under our assumptions, could only come from the time derivative of E in the Ampere-Maxwell law. Since our induced E is constant (because dI/dt is constant) this term is zero. Similarly for the self-induced countercurrent - it is at most a constant term that disappears when we take the time derivative of B.

    Thus it appears to me that the quasistatic approximation to the emf induced by a steadily increasing current is only approximate if the wire cannot be assumed to be electrically neutral - then we have charges piling up resulting in a time-dependent E-field and so on. The approximation to the magnetic field will be off by a constant term, the self-induced current.

    But on the other hand, if we have a sinusoidal current, even IF the wire is taken to be neutral, the curl of E will still have a time-dependent component, thus a non-zero time derivative in the Ampere-Maxwell equation and the self-induced current, and so on to the nth time derivative until the 1/c term in the curl of B makes it negligible.

    Is this theoretically correct, or is there some other time-independent assumption I'm neglecting?

  2. jcsd
  3. Jan 14, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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