Just some correction on your usage of words as a physics student - changing magnetic flux linkage in a coil induces an emf in the coil which causes a current to flow around a coil if it is part of a complete circuit. The induced current in the coil will produce a magnetic field that opposes the change in magnetic flux through the area enclosed by the coil. This is Lenz’s law, not Faraday law.
Eddy current is no different from the induced current in the coil of a complete circuit except the name given to it except that it exists within a slab of conductor.
The swirling eddy current and the induced current in the coil of a complete circuit are the “result” of changing magnetic flux linkage or “cutting” of magnetic flux.
When a conducting plate is allowed to swing between two unlike magnetic poles, the induced “uneven emf” due to the cutting of the magnetic flux will “give rise” to the swirling eddy current.
One thing to note here is that as an A-level physics student, you should know how to explain the damping effect of the swinging disc using only Lenz’s law or only Faraday’s law.
Most students have no problem in explaining the damping effect via Lenz’s law which explains how the magnetic force arises due to the eddy current and acts in the direction opposite to the direction of motion of the disc.
The diagram shows what happens to the conducting plate as it enters and leaves the magnetic field.
As only part of the conducting plate just enters the magnetic field from the left, the magnetic flux linkage with the conducting plate increases, an induced e.m.f. is created in that part but not in the part that has not yet entered.
The induced e.m.f. would “create” currents in the conducting plate itself. These currents are known as eddy currents that flow in a circular fashion inside the conducting plate.
Lenz’s law predicts that the induced currents that flow counterclockwise direction in the conducting plate (shown in the diagram).
Only the right-hand side of the current loop is in the field, using Fleming left rule, we can predict a magnetic force acts on the conducting plate to the left which is opposite to the direction of motion to slow down the plate’s speed. This magnetic force is the damping force.
When the conducting plate is completely inside the field, there is no eddy current if the field is uniform, since the magnetic flux linkage with the conducting plate remains constant in this region.
But when the conducting plate leaves the field on the right, the magnetic flux linkage with the conducting plate decreases, causing an eddy current in the clockwise direction that, again, experiences a magnetic force to the left, further slowing the motion.
As Joinedup described greatly that it is neither good nor bad, eddy currents, like other electrical currents, cause heating in the conducting materials. This means that useful energy will be converted thermal energy via heating, so energy is dissipated.
The current that is induced in a coil can also cause heating in the coil. Although generators can be said to produce power (induced emf and current), this does not mean the current is good. If this current flows in a wire, it will also cause heating in the wire and energy will still be “lost” in the form of thermal energy.
Sorry for a lengthy description.