Experiment on magnetic line of force Say hypothetically the electrical current is flowing through the solenoid which is wrapped around a colossal electromagnet which is approximately 1 lightyear long. (Assume there is no resistant so no power loss and negate effect of gravity)
Q1:How long would the magnetic lines of force takes to form if any?
Q2: How do the magnetic line of force from both end of the electromagnet knows when/where to meet?
 A: This is actually an interesting question because you're asking about a solenoid rather than a simple wire. That means there are actually a few different things going on here.
All of the electromagnetic signals at work here travel at $c$. The first thing to happen is, when you connect the battery at one end of the solenoid, current starts flowing in the circuit near the switch, and the signal of that event travels along the wire at $c$. Since your wire coils around the solenoid rather than shooting straight along, the wire will be quite a bit longer than the solenoid itself, and the exact length depends on the diameter of your solenoid and how tightly it is wound. With a very tightly wound solenoid of large diameter you could have thousands or tens of thousands times the wire length than the length of your solenoid... meaning the switch signal itself could take tens of thousands of years to reach the far end. Yikes!
On the other hand, the change of current in the wire changes the magnetic field that the wire generates, and that field travels at $c$ as well, but it propagates in free space rather than along the wire. When you flip the switch at one end, it generates a pulse in the electromagnetic field that travels to the end of your 1ly solenoid in one year, causing all the usual inductance along the way.
The magnetic field also realigns the magnetic domains in the ferromagnetic core of the solenoid, and as far as the effects of the aligned domains is distinguishable from the magnetic field from the wire, that change also propagates at $c$.
So far, I haven't answered either of your two sub-questions, so here we go:
A1: The magnetic lines of force form at a given location as soon as the change in the magnetic field reaches that location. So at the surface of the wire just next to the switch, it is immediate; half way up the solenoid, or really half a light year in any direction, it happens six months later.
A2: The magnetic lines of force don't have to "meet" anywhere because the magnetic field is continuous everywhere. When you turn on the solenoid, all you are doing is propagating a change in the field, and those changes are continuous as well: by which I mean, the magnetic field strength at a given radius from the moving charge (in the wire, in this case) is either 0, or it is equally non-zero at a given radius from the moving charge. In other words, the magnetic field is already "connected" to itself and nothing has to "meet up." There is always a continuous 3D equipotential surface.
