Eddy currents of a thin wire vs. a large plate? In many examples such as this:

I noticed that most cases where Eddy currents are of focus, or have a considerable effect, would be with examples having a large conductive area perpendicular to the magnetic field, such of a plate or a disc etc...
If I compare it to wires very thin(regardless of length) there aren't any Eddy currents? I fail to understand the difference with this set-up:

Are there Eddy currents to this case as well?
 A: This video is the best illustration of the effect that I have seen because it introduces a third type of pendulum as well as the normal plane metal sheet (1) and the metal sheet in the form of a comb (2).  It is a sheet with slots in it (3).

The plane metal sheet is your first example and the metal sheet in the form of a comb is your second example.  The third sheet is the intermediate type.
When a conductor passes at right angles to a magnetic field, an emf is induced - Faraday's Law.  This happens in each of the sheets because of the force produced by the magnetic field on the moving mobile charge carriers in the metal plates.
If there is a conducting path, currents are induced whose magnitude depend on the magnitude of the induced emf and the resistance of the conducting path.  
The induced current tries to oppose the motion producing it - Lenz's Law.
The larger the current the greater the opposition.
In the demonstration the opposition is greatest for sheet 1 and least for sheet 2.
I think that the diagrams speak for themselves in showing why it is the induced (eddy) currents are much bigger in sheet 1 than sheet 2 and so much bigger than in sheet 3.  It is the resistance of the conducting paths which changes due to the different sheet geometries.
Note that the emf induced in sheet 1 is less than that induced in sheet 2 and yet because the resistance of the conducting paths in sheet 1 are so much less than in sheet 2 the induced (eddy) currents (opposition to motion) are so much larger.
