# I Induced magnetic field

1. May 9, 2017

### 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.

2. May 9, 2017

### gleem

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.