Does the shape of a conductor affect the induced magnetic field?

[vibe3]

If an arbitrary shaped conductor is moving through a steady-state magnetic field, $\mathbf{B}(\mathbf{r})$, is it true that the field induced in the conductor will be proportional to $\mathbf{B}$? IE:

$$\mathbf{B}_{induced}(\mathbf{r}) = M \mathbf{B}(\mathbf{r})$$

where $M$ is a 3-by-3 constant matrix? Or is this simply a first-order approximation to the induced field? Does anyone know of any texts or references which treat this problem? Thanks.

 

[mfb]

As you consider an induced magnetic field, I guess your conductor is a closed loop (or at least has some circular current paths)?

You cannot evaluate the field point by point. The induced field at one point will depend on the magnetic field everywhere else (and the velocity of the conductor everywhere).