Magnetic Field Produced by Solenoid

Question

I was reading about solenoids and came to know that the magnetic field strength of a solenoid is greatly increased by

1. Increasing the number of turns in the solenoid coil (directly proportional to square of number of turns);
2. Using a soft iron core;
3. Increasing the current flowing through the solenoid;
4. Reducing the spacing between the turns of the coil.

So if the coil is made tighter and tighter, the field will become stronger because flux leaks are reduced.

But say we reduced the gap to such an extent that the turns will be as good as in contact. In other words,

If I take a hollow cylinder and connect two of its ends to opposite terminals of a battery, what will happen to the magnetic field?

From the above reasoning it appears as if it would increase, but again I presume that current will take shorter paths and therefore the cylinder will become the equivalent of a parallel combination of many wires of thickness $dx$ ($dx$ would be equal to width of a metal lattice, I presume), which will not behave as a solenoid but rather like a really weak bar magnet with no field line in the centre.

Answer 1

A theta pinch, is similar to what you describe. It is essentially a sheet of metal folded to form a cylinder. Usually it is produce a very intense magnetic field for a short time since the current is pulsed.

Reference

Answer 2

The hollow cylinder will not generate a solenoid-like magnetic field, as you predicted. The current will move parallel to the cylinder's axis and not in circles around the circumference.

You are correct about the decreased spacing between the coils resulting in stronger magnetic fields. This is why wire that is manufactured for creating electromagnets is coated with extremely thin insulation. This allows for much tighter windings due to there being less insulation getting between the wires.