Ampere’s circuital law:

Application of Ampere’s circuital law in magnetic circuit:
Ampere’s circuital law is quite handy in determining field strength within a core of a magnetic material. Due to application of mmf, the tiny dipole magnets of the core are aligned one after the other in a somewhat disciplined manner. The contour of the lines of force resembles the shape the material. The situation is somewhat similar to flow of water through an arbitrary shaped pipe. Flow path is constrained to be the shape of the bent pipe. For an example, look at the sectional view (figure A & B) of a toroidal magnetic circuit with N number of turns wound uniformly as shown below. When the coil carries a current i, magnetic lines of forces will be created and they will be confined within the core as the permeability of the core is many (order of thousands) times more than air.

Take the chosen path to be a circle of radius r. Note that the value of H will remain same at any point on this path and directions will be always tangential to the path. Hence by applying Ampere’s circuital law to the path we get the value of H to be 2NI/πr. If r is increased from a to be b the value of H decreases with r. a and b are respectively the inner and outer radius of the toroidal core.

fig(A)..fig(B)