Step 1: Understand electromagnetic induction in moving conductor.
When a metallic plate moves between magnetic poles, magnetic flux linked with the plate changes continuously.
Step 2: Eddy currents are induced.
Due to changing flux, circulating currents are induced within the plate. These are called eddy currents.
Step 3: Apply Lenz's Law.
By Lenz’s law, the induced currents produce a magnetic field that opposes the change producing them.
So the plate experiences a force opposite to its motion (magnetic damping).
Step 4: Conclusion.
Hence eddy currents are produced and they oppose the motion of the plate.
Final Answer:
\[
\boxed{\text{(C) eddy currents oppose the motion of the plate}}
\]