Induced Magnetic Field: Moving Arbitrary Conductors in Nonuniform Fields

[vibe3]

If I have some arbitrary conductor moving through a (nonuniform) magnetic field $\mathbf{B}(\mathbf{r})$, 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.

 

[gleem]

If I have some arbitrary conductor moving through a (nonuniform) magnetic field B(r)B(r)\mathbf{B}(\mathbf{r}), would the induced field in the frame of the conductor be something like:

BIND(r)=TB(r)BIND(r)=TB(r)​

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.