What does the strength of the magnetic field inside a circular conducting coil depend on?

A circular conducting coil is called a solenoid; the magnetic field within the center of the solenoid is approximately uniform, and by Ampere's Law, its strength B is proportional to the permeability of the surrounding material (e.g. air, vacuum, etc.) mu , the current running through the coil I, and the number of turns of the coil N divided by the length of the solenoid L:B = mu I N/L
For an infinitely long solenoid (of course only a theoretical concept, not something we could actually build), we write it instead in terms of a density of loops, n:B = mu_0 I n For real solenoids, this is only an approximation, but it's often a quite good one.Thus, the magnetic field inside the coil will be stronger if there is more current (higher I), if the material is more permeable (higher mu ), or if the coil is more tightly wound (higher n or higher N/L).
 
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html