For Eddy Currents, must the conductor be large in area size?

Question

Consider the following classical configuration:

Let's change a few things, lets assume that:

1. There is no applied current on the wire & it's stationary.
2. The external magnetic field was from a electromagnet that varies over time.

The wire is a thin piece of conductor surface, and the varying magnetic field is perpendicular to it's surface, wouldn't there be eddy currents on the surfaces to react to the change in magnetic field?

As per Eddy current's description:

Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. - [2]

Eddy currents don't depend on the size of an area, but on the continuity of conductivity of that area?

[2]: https://en.wikipedia.org/wiki/Eddy_current#:~:text=Eddy%20currents%20(also%20called%20Foucault's,perpendicular%20to%20the%20magnetic%20field.

Answer 1

wouldn't there be eddy currents on the surfaces to react to the change in magnetic field?

Of course they would. That is a basic principle of magnetic shielding against alternating magnetic fields. Moreover, the eddy fields have a certain intrusion depth (called the Skin depth) that depends on the frequency of the varying field (assuming that we only consider a single sinusoidal variation) and the conductivity of the material. The higher the frequency, the smaller the intrusion depth/Skin depth, whereas static magnetic fields have infinite depth (assuming an idealistically non-magnetic material, i.e. $\mu_r=1$). The fact that the dynamic magnetic field gets expelled from the conductor could be considered as kind of a diamagnetic effect, and similarly to those it can lead to magnetic levitation for strong fields and appropriate geometric designs (see for example this video). The expulsion can also be considered a manifestation of Lenz' law, that is, as you properly phrased it, the currents "react to the change in magnetic field".

Eddy currents don't depend on the size of an area, but on the continuity of conductivity of that area?

They depend on the size of the area that is permeated by the magnetic field - and on the conductivity. Of course, this assumes that the conductor is large compared to the size of high-intensity region of the magnetic field. If the conductor is smaller than this region, there will be boundary effects in that the currents will be limited to the boundary of the conductor, and hence, be reduced compared to a "full-sized" conductor. Similarly, the reaction force will be lower if the conductor only crosses a small part of the magnetic field.