When a bar magnet is pushed into a coil of copper wire, there are certain phenomena that occur based on electromagnetic induction. Let's discuss the process step by step:

1. Magnetic Field:
The bar magnet has a magnetic field around it, with a north pole and a south pole. The magnetic field lines extend from the north pole to the south pole.

2. Induced Electric Field:
As the bar magnet is pushed into the coil, the magnetic field lines pass through the coil of wire. According to Faraday's law of electromagnetic induction, a change in the magnetic field through a coil of wire induces an electric current within the wire. In this case, the magnetic field lines are increasing within the coil.

3. Lenz's Law:
According to Lenz's law, the induced current flows in such a way as to oppose the change that produced it. In this case, as the magnetic field lines are increasing within the coil, the induced current will flow in a direction to create a magnetic field that opposes the increasing magnetic field of the bar magnet.

4. Direction of the Induced Current:
Based on the right-hand rule, when the north pole of the bar magnet enters the coil, the induced current flows in a direction such that the face of the coil facing the approaching north pole of the magnet becomes a south pole. This means that the side of the coil closest to the magnet's north pole will have an induced south pole.

Explanation for the given options:

a) The needle of the galvanometer shows no deflection: This option is incorrect because an induced current is produced in the coil due to the changing magnetic field, which will cause a deflection in the needle of the galvanometer.

b) The needle of the galvanometer shows a momentary deflection towards the right: This option is incorrect because, according to Lenz's law, the induced current flows in a direction to oppose the change in the magnetic field. In this case, the induced current will create a magnetic field that opposes the increasing magnetic field of the bar magnet, causing a deflection towards the left.

c) The needle of the galvanometer shows a momentary deflection towards the left: This option is correct because the induced current flows in a direction to oppose the increasing magnetic field of the bar magnet. As a result, the needle of the galvanometer will momentarily deflect towards the left.

d) None of these: This option is incorrect based on the explanation provided above.

In conclusion, when a bar magnet is pushed into a coil with its north pole entering first, the needle of the galvanometer connected to the coil will show a momentary deflection towards the left.