160517-1509 EDT
You are listed as a student. And you listed a code year. Therefore, I assume you are studying to become an electrician.
First, you need to define what is a solenoid. A quick Internet search produced
https://en.wikipedia.org/wiki/Solenoid . The word solenoid can have different meanings.
From what you indicated in your question I am not clear on what is your question. Before pursuing what you want to work with I will present some basics.
A changing magnetic field relative to a wire will induce a voltage in the wire. This changing field can be produced by moving a magnetic field relative to a fixed position conductor (lay a wire on a table, connect the wire to a very sensitive DC meter, move a very strong hardware store magnet to the wire, and you may see a short duration small voltage spike --- I used a Beckman DVM that resolves 10 microvolts and saw a peak of 60 micro-V), or the magnetic field can be fixed and wire moved (a DC generator). The induced voltage can be described by the equation v = K*N*dPhi/dt where v is the instataneous voltage with respect to time, K is some constant, N is the number of turns linking the magnetic field, and dPhi/dt is the rate of change of magnetic flux with respect to time (speed). The faster the change the greater is the induced voltage.
I have a 30 turn coil wound on a 18" square wood frame. Making quick motions in the earth's magnetic field I can produce possibly 1 or 2 millivolts into a Fluke 27 meter.
With a small 1500 turn air core coil and an LED across the coil I could not produce enough magnetic coupling from my magnets to produce any light.
You need good magnetic coupling, many turns in your coil, and a rapid change of magnetic flux to provide any LED light.
A solenoid actuator designed to produce motion of a plunger will have good magnetic coupling, and a moderate number of turns. The plunger is not usually a permanent magnet and thus does not produce a very strong magnetic field, probably near none. Voltage is only produced when the magnetic field is changing. Voltage does not come from a solenoid plunger, but would come from the coil if you were trying to make the solenoid a generator.
Using the above as background can you clarify your question?
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