transformerDesign
Fundamentals of Magnetics
Magnetic Properties in Free Space
To use the “right hand rule” to determine the line of flux around a straight conductor. That is when the conductor is grasped with the right hand, so that the thumb points in the direction of the magnetic lines of force.
Simple Transformer
The flux diverges from the ends of the primary coil. The primary is connected to the source and carries the current that establishes a magenetic field. The other coil is open-circuited. Notice that the flux lines are not common to both coils. The difference between the two is the leakage flux; that is, leakage flux is the portion of the flux that does not link both coils.
Magnetic Core
When the demagnetized, ferromagnetic material is exciting with an external magnetizing force, H. It will increase slowly from zero. Shown as below.

At first, the flux density increases very slowly up to point A. Then, increases rapidly up to point B, and then, alomost stops increasing. Point B is called the knee of the curve. At point C, the magnetic core material has saturated. And from that point on, the slope of the cuve is shown in equation.
Now, the coil is behaving like as if it had an air-core, which means has the same permeability as air.
Hysteresis Loop(B-H Loop)
When the magnetic material is taken through a complete cycle of magnetization and demagnetization, the results are shown.

Extra Reading
What is a Planar Transformer
A planar transformer is an electrical deveice that transfers power from one circuit to another.