Magnetic Circuital Laws
Ampere’s law:
The magnetic field intensity H around a closed contour C is
equal to the total current passing through any surface S linking that
contour which is known as Ampere’s law as shown in equation
∫H.dl = Σi
where H is the magnetic field intensity at a point on the contour
and dl is the incremental length at that point.
Suppose that the field strength at point C distant r meters from
the center of the conductor is H. Then it means that if a unit N-pole
is placed at C, it will experience a force of H Newton. The direction
of this force would be tangential to the circular line of force passing
through C. If the unit N-pole is moved once round the conductor
against this force, then work done, this work can be obtained from
the following releation:
Work = Force*distance = H * 2π *r (1.2)
The relationship between the magnetic field intensity H and the
magnetic flux density B is a property of the material in which the
field exists which is known as the permeability of the material;
Thus,
B = uH (1.3)
where u is the permeability.
In SI units B is in webers per square meter, known as tesla (T),
and In SI units the permeability of free space, Vacume or
nonmagnetic materials is 7
u0 = 4π *10^-7 . The permeability of ferromagnetic material can be
expressed in terms of its value relative to that of free space, or u u0 *ur
Where ur is known as relative permeability of the material. Typical
values of ur range from 2000 to 80,000 for feromagnetic materials
used in transformers and rotating machines. For the present we
assume that ur is a known constant for specific material, although it
actually varies appreciably with the magnitude of the magnetic
flux density.
Source (pdf)
http://faculty.ksu.edu.sa/eltamaly/Documents/Courses/EE%20339/
MAGNETIC%20CIRCUITS.pdf
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Magnetic Circuital Laws
Consider the magnetic circuit in the last section with an air gap of
length lg cut in the middle of a leg as shown in figure (a) in the diagram
below. As they cross the air gap, the magnetic flux lines bulge outward
somewhat as illustrate in figure (b).
The effect of the fringing field is
to increase the effective cross sectional area Ag of the air gap. By
Ampere’s law, we can write
According to Gauss’ law in magnetics,
That is, the above magnetic circuit with an air gap is analogous
to a series electric circuit. Further, if we regard Hclc and Hglg as
the “voltage drops” across the reluctance of the core and airgap
respectively, the above equation from Ampere’s law can be
interpreted as an analog to the Kirchhoff’s voltage law (KVL)
in electric circuit theory, or
The Kirchhoff’s current law (KCL) can be derived from the
Gauss’ law in magnetics. Consider a magnetic circuit as shown
below. When the Gauss’ law is applied to the T joint
in the circuit, we have
Having derived the Ohm’s law, KVL
and KCL in magnetic circuits, we can solve very complex magnetic
circuits by applying these basic laws. All electrical dc circuit analysis
techniques, such as mesh analysis and nodal analysis, can also be
applied in magnetic circuit analysis. For nonlinear magnetic circuits
where the nonlinear magnetization curves need to be considered,
the magnetic reluctance is a function of magnetic flux since the
permeability is a function of the magnetic field strength or flux density.
Numerical or graphical methods are required to solve nonlinear
problems.
Source (pdf)
http://services.eng.uts.edu.au/cempe/subjects_JGZ/eet/eet_ch4.pdf