If an arbitrary shaped conductor is moving through a steady-state magnetic field, [itex]\mathbf{B}(\mathbf{r})[/itex], is it true that the field induced in the conductor will be proportional to [itex]\mathbf{B}[/itex]? IE:
[tex]
\mathbf{B}_{induced}(\mathbf{r}) = M \mathbf{B}(\mathbf{r})
[/tex]
where [itex]M[/itex] 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.
[tex]
\mathbf{B}_{induced}(\mathbf{r}) = M \mathbf{B}(\mathbf{r})
[/tex]
where [itex]M[/itex] 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.