1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:


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


    The proposed solution used Faraday's law of induction:

    Method 2:


    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:


    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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook