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I Induced magnetic field

  1. May 9, 2017 #1
    If I have some arbitrary conductor moving through a (nonuniform) magnetic field [itex]\mathbf{B}(\mathbf{r})[/itex], would the induced field in the frame of the conductor be something like:
    \mathbf{B}_{IND}(\mathbf{r}) = T \mathbf{B}(\mathbf{r})
    where T is some diagonal matrix whose entries are related to the susceptibilities of the conductor?

    I'm having trouble finding any reference on this other than a wire moving through a uniform field with some velocity.
  2. jcsd
  3. May 9, 2017 #2
    The induced field in the conductor is an electric field not a magnetic field. Susceptibility of the conductor is irrelevant.

    The voltage or EMF = C E⋅dl where E is the electric field in the conductor and dl is an elemental conductor length.
    For a varying magnetic field B(x,y,z) and a conductor C moving with velocity v the
    EMF = C
    (vxB)⋅dl where the integral is taken around the conducting loop C.
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