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Induction in an inflating loop in constant B?

  1. Feb 17, 2008 #1
    A loop is made from a conductive wire. The wire moves, so the area inside the loop is time dependent: S=S(t)
    There is a constant homogeneus magnetic field B directed perpendicular to the wire and we are supposed to calculate induced voltage.

    In my opinion there is no electric field and no voltage, since there field B is
    constant. However there is a magnetic force experienced by charges moving in magnetic field:

    Method 1:

    F=e*B*v

    If this force is integrated over the loop to gain work on a charge e after 1 circle, we get:

    A=-e*B*dS/dt


    The proposed solution used Faraday's law of induction:

    Method 2:

    U=-dfi/dt=-d(B*S)/dt=-B*dS/dt

    I think that this is a misuse of the law, since corresponding Maxwell's equation can be
    used only for fixed loop, but changing magnetic field. However the work gained by a charge completing one circle is exactly the same as with previous method:

    A=e*U=-e*B*dS/dt

    My question is:

    Is the method 2 realy incorrect? If yes, why is the work the same? If no, how do we prove that Faraday's law can be used in case of constant B and changing loop area?
     
    Last edited: Feb 17, 2008
  2. jcsd
  3. Feb 18, 2008 #2

    clem

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    Science Advisor

    Faraday's works for any change in the flux.
    For constant B and changing area, it is often derived for a rectangle in elementary texts.
    It is derived for an arbitrary change in the area in more advanced texts.
     
  4. Feb 19, 2008 #3
    I found some related texts and I hope I understand the problem now: it seems that
    in case of the moving loop the "induced voltage" is not an integral of a real electric field, but an integral of a fictional electric field, that would do the same work on a circling charge.
     
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