Visualising the magnetic field How can we visualise the magnetic field?How to visualise magnetic field due to current carrying conductor having poles(like north and south for ordinary magnetic).
Can we determine the north and the
south of the magnetic field produced by
the current.
 A: 
How can we visualise the magnetic field?

Easy draw little lines coming out of one end of a magnet, and follow some rules (like lines must be closed, these lines tend to "repel" each other if possible and do not cross). From this we can tell a lot about the magnet and the field around it. But in reality we usually solve for the magnetic field first and then draw the lines to visually represent the solution.

How to visualise magnetic field due to current carrying conductor

The solution to a solenoid usually works out to be almost the exact same as the solution to a similar bar magnetic.
Using Maxwell's equations we can say that:
$$
\nabla \cdot \vec B = 0
$$
This means that there are no divergences in the magnetic field, i.e. the quantity $\vec B$ cannot have sources or sinks. So it acts like a tank of water, there can be flow but no hose pipes pumping water in or sucking it out.
Another one of Maxwell's equations state that:
$$
\nabla \times \vec B = \mu \vec J + \epsilon \mu  \frac {\partial \vec E}{\partial t}
$$
Which says that you can create (a flow of water) curls in the field $\nabla \times \vec B$ by using a flow of current density $\vec J$ or by using an electric field changing in time $\frac {\partial \vec E}{\partial t}$.
So inside a bar magnet there are a load of tiny unpaired electrons spinning around in circles creating a load of tiny little current flows which in turn create a magnetic field effect (a flow in the $\vec B$ field).
In a solenoid the result is the exact same except instead of a load of tiny little pumps there is one huge pump pumping the $\vec B$ field.

Can we determine the north and the south of the magnetic field produced by the current.

Yes using the right hand rule we can say that using your right hand have your fingers follow the current flow and your thumb will be pointing in the direction of the north pole. (This is present in the mathematics, as the right hand rule is built into the definition of the cross product \nabla \times \vec B)
Visualising the field, if they existed and you have a magnetic monopole, imagine a small particle in the water analogy. Place this monopole at one end of the bar magnet and trace its path, it will travel around a closed loop, this represents one of the magnetic field lines one often sees drawn when representing magnetic fields. 
A: First, one would have to define what the north and south pole should be. In practice this is not so clear.
Actually, the current loop is the more fundamental concept for producing a magnetic field. E.g., a bar magnet can simplified be imagined as a composition of a huge number of current loops. Their magnetic fields add up to the overall field of the bar magnet.
The current loop on the other hand defines more a north-south-direction than something with two poles. Here I refer to the direction of the B-field in the middle of the current loop.
