Fields due to Currents
A Swedish physicist called Oersted discovered that currents in wires produced magnetic fields.

If the current carrying wire is wrapped into a coil, or solenoid, then the field is very similar to a bar magnet.

The field produced by a solenoid, without a core, is calculated using    

B = Field strength (T)   N = Number of turns   I = Current (A) and    is a constant known as the permeability of free space.

If the solenoid has another material in its core, e.g. iron, then the permeability is different. The permeability of iron is very large so lots of flux is produced.

Magnetic Circuits.
In most magnetic machines (transformers, motors etc.) we would not let our flux leak away so wastefully. The core is in the form of a ring, usually made of laminated iron. Being iron we get lots of flux and it stays inside the iron traveling round it.

The Permeance, ,  of the magnetic circuit is analogous to the conductance of an electrical circuit. The greater the permeance, the more easily the flux can flow.

in both cases  "how easy it is to flow" = "something flowing"  divided by "something pushing"

The permeance of the magnetic circuit depends on the permeability of the core material, its cross sectional area and its length.