If a magnet is completely inside a solenoid, but is moving, Does this induce an emf? I am not addressing here the case when the magnet is approaching the solenoid or when it is moving away from it. I am asking about that part of the journey when the magnet is inside the solenoid completely but still moving, so in this situation, Do this induce an emf? If the answer is no as I believe it is the case, then why no? Why the magnetic flux inside the solenoid isn't changing even though the magnet is moving?
 A: There is no emf if the magnet's length is much shorter than that of the solenoid, and the magnet is well inside the solenoid, so not approaching either end. This is because the number of turns linked by the magnet's flux doesn't change as the magnet moves. However, as the magnet approaches one end of the solenoid (even though it's still inside), fewer and fewer turns will be linked by the magnet's flux, so there is a non-zero rate of change of flux linkage, and therefore an induced emf.
[Another way of looking at what's going on is to add the emfs (if any) induced in the individual turns. When the magnet is moving along in the central region of the solenoid no emfs are induced in the turns around the magnet's centre, because the flux linked with these turns is constant (for a short while). But there are equal and opposite emfs induced in turns around the magnet's poles and beyond as the flux linkage increases at and beyond one pole, but decreases at and beyond the other.]
To see all this clearly, draw a solenoid (a long, thin rectangle will do) and a short magnet inside it. Then draw a few representative magnetic field lines for the magnet. [Don't forget that magnetic field lines are continuous closed loops: they emerge from the North Pole, curve round through the air (penetrating the solenoid 'walls'), enter the South Pole and continue, going from South Pole to North Pole inside the magnet.] This should make the paragraph above easier to understand.
A: Let us assume that the copper coils of the solenoid do not alter the magnetic field of the magnet.
Let the solenoid start at $x$=0 and end at $x$=$L$. Let us say that the magnet is at a position $x$=$M$, with $M<L/2$ (we can deal with the situation $M>L/2$ analogously). Then, we can divide the solenoid into three parts, from 0 to $M$, from $M$ to $2M$, and from $2M$ to $L$. The motion of the magnet has opposite effects in the first and second sections, due to symmetry. What generates a net emf is the segment of solenoid from $2M$ to $L$.
It is like having a solenoid between $2M$ and $L$, with the magnet outside it, and moving. It is like the first and second segments do not exist at all. And the magnet is moving outside the last segment, so it generates emf.
If $M$ is large with respect to the size of the magnet and the diameter of the solenoid, the segment from $2M$ to $L$ is not affected too much by the motion of the magnet.
A: If the magnet is inside the coil cavity and moving that means the magnetic flux associated with the coil is changing with respect to time ,so from faradays law the emf should be induced to the coil.
if you think iam incorrect then put the question clearly once again as i think that the above answer is most relevent to the question asked by you
