Magnetic flux inside solenoid Suppose that I have a small coil that is moved at a steady rate into a solenoid. The solenoid already has a current passing through (basically, it is an electromagnet). The small coil starts beyond the solenoid, moves towards it, into it, then out of it through the other end. What is the magnetic flux inside the solenoid? (i.e. What is the shape of the magnetic flux vs. time graph inside the solenoid?)
Once the coil is completely inside the solenoid, the magnetic flux is constant as the magnetic field inside is uniform. However, is the magnetic flux inside the solenoid increasing when the coil approaches, or decreasing? I personally think it is decreasing because the coil induces a field to oppose the field of the solenoid, while the field of the solenoid is unchanging. Hence, the field inside the solenoid is partially cancelled out, and the magnetic flux is decreasing. However, I was told that I am wrong. Can anyone explain why?
 A: as the coil approaches the solenoid the field intensity through the coil keeps on increasing hence increasing flux,in order to oppose this, a magnetic field is produced by the coil in opposite direction to the solenoid's field hence as it comes closer to the solenoid the intensity of field produced by coil also increase to oppose the increasing solenoid field flux.As you told this would imply that the field inside the solenoid has DECREASED AND IS STILL DECREASING as the coil approaches it because of the field lines of the coil entering the solenoid from the opposite direction and the coil's field flux is still increasing inside the solenoid.In order to OPPOSE this the solenoid will try to increase its field strength and hence flux will increase by Lenz law inside the solenoid to keep its original field intensity the same.All this happens in a very short time.
THE MAGNETIC FIELD INSIDE THE SOLENOID CHANGES but it happens momentarily as the solenoid restores its original field.
Lenz’s law tells us that the induced EMF will try to “fight” this: the EMF that
is induced will tend to drive currents which 'oppose'(as in the solenoid due to the coil-mutual inductance) the change in magnetic flux. For this
setup, this means that the EMF will oppose the decrease in field strength of the solenoid inside the solenoid — it will drive a current which
tries to prevent B from changing it will reinforce its field.
A: If the ends of the coil are shorted (so that current can flow in the coil), then as it enters the solenoid, the changing flux through the coil will produce a current in the coil that produces a field which opposes the increase in the flux. This induced field will tend to reduce the net flux through the solenoid.  That produces an emf in the solenoid which works with the external power supply to try to maintain the original flux through the solenoid. All of these things depend on the rate of change, so there will be an increase in the current through the solenoid as the net flux is decreasing.
