If we have a copper of length l, how would you arrange it to obtain the maximum inductance?
Inductance is a measure of the size of the back electromotive force that given inductor will induce on itself. The inductance depends upon the physical structure of the circuit element and not upon the current or voltage across the inductor.
So, to maximize the indictance of a copper wire it needs to be arranged such that the electro-magnetic fields produced by the wire sum together. That configuration is a coil, or a solenoid.
Let's try to solve this problem on the example of simple coils with cylindrical shape and a single layer.
The indicative values of the maximum inductance that can get in the coils with a layer, depending on the diameter of casing, are given below:
Diameter of casing [mm]:10 Maximum inductance [microH]:30
Diameter of casing [mm]:15 Maximum inductance [microH]:50
Diameter of casing[mm]:20 Maximum inductance [microH]:100
Diameter of casing[mm]:30 Maximum inductance [microH]:200
Diameter of casing[mm]:50 Maximum inductance [microH]:500
Inductance of such coils can be determined with one of these relationships:
L=D^2*n^2/(100*l+44D), where n = number of turns;D = diameter,in cm; w = length winding,in cm.
In order to increase inductance and decrease the number of turns, coils can be provided with a core of a magnetic material . The core is provided with groove or fixed in a cylindrical plastic screw piece cap for adjustment of position inside the coil.Through this is adjusted slightly the value of inductance, also.