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If we change the magnetic flux through a coil -->

Will any current flow through this coil if it's two terminal is not connected to any kind of load, i.e - It is not in a closed loop.

If the answer is No,then please tell me how it will oppose the change of magnetic flux? As we know that (from Lenz's law), the direction of current will oppose the change of the flux, but if no current passes through it, how it will oppose the change of the flux?

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Neither Faraday's law nor Lenz's law says that a current will be induced to oppose the change in magnetic flux. Faraday's law says that an electromotive force (emf) will be induced in the coil. According to Lenz's law, the direction of the emf is such that if this emf results in a current (i.e. the loop isn't open circuited), this current will oppose the change in magnetic flux. If the loop is not closed, naturally no current will flow, even though there is an induced emf.

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Perhaps looking at the question in terms of energy might help.

If the coil is part of a conducting a magnet moving towards will generate an emf in the coil (Faraday) which in turn induce a current in the circuit.
That induced current produces a magnetic field which means that for the magnet to move into the coil at constant speed a force must be applied to the magnet (Lenz).
That force is doing work moving the magnet at the same rate as ohmic heating is being produced due to the coil circuit having resistance (Conservation of energy).
If the force between the coil and the magnet was not repulsive heat would be generated in the coil without and work being done.

Now with the situation that you are considering with an incomplete circuit an induced emf is produced but no current flows and there is no opposition.
Why not?
No heat is being generated in the incomplete coil circuit and no work needs to be done to keep the magnet moving at constant speed and so no force is needed to keep the magnet moving at constant speed.
So in this situation Lenz is redundant.

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