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DK4141_C01.fm Page 1 Tuesday, January 18, 2005 11:10 AM 1 Fundamentals of Magnetic Theory This chapter gives a brief review of the basic laws, quantities, and units of magnetic theory. Magnetic circuits are included together with some examples. The analogy between electric and magnetic circuits and quantities is presented. Hysteresis and basic properties of ferromagnetic materials are also discussed. The models of the ideal transformers and inductors are shown. 1.1 Basic Laws of Magnetic Theory The experimental laws of electromagnetic theory are summed up by the Maxwell equations. In 1865, after becoming acquainted with the experimental results of his fellow Englishman Faraday, Maxwell gave the electromagnetic theory a complete mathematical form. We will present specific parts of the Maxwell equations: Ampere’s law, Faraday’s law, and Gauss’s law, which together with Lenz’s law are the basis of magnetic circuit analysis. These are the laws that are useful in the design of magnetic components for power electronics. 1.1.1 Ampere’s Law and Magnetomotive Force When an electrical conductor carries current, a magnetic field is induced around the conductor, as shown in Fig. 1.1. The induced magnetic field is characterized by its magnetic field intensity H. The direction of the magnetic field intensity can be found by the socalled thumb rule, according to which, if the conductor is held with the right hand and the thumb indicates the current, the fingers indicate the direction of the magnetic field. The magnetic field intensity H is defined by Ampere’s law. According to Ampere’s law the integral of H [A/m] around a closed path is equal to the total current passing through the interior of the path (note that a line above a quantity denotes that it is a vector): ∫ H ⋅ dl = ∫ J ⋅ d S l Copyright 2005 by Taylor & Francis Group, LLC S (1.1) DK4141_C01.fm Page 2 Tuesday, January 18, 2005 11:10 AM 2 Inductors and Transformers for Power Electronics Total current i Total density J i1 i2 i3 l FIGURE 1.1 Illustration of Ampere’s law. The MMF around a closed loop is equal to the sum of the positive and negative currents passing through the interior of the loop. i4 Surface S with area Ac H where H is the field intensity vector [A/m] dl is a vector length element pointing in the direction of the path l [m] J is the electrical current density vector [A/m2] dS is a vector area having direction normal to the surface [m2] l is the length of the circumferenc...
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Fundamentals of Magnetic Theory
This chapter gives a brief review of the basic laws, quantities, and units of
magnetic theory. Magnetic circuits are included together with some examples.
The analogy between electric and magnetic circuits and quantities is pre
sented. Hysteresis and basic properties of ferromagnetic materials are also
discussed. The models of the ideal transformers and inductors are shown.
1.1 Basic Laws of Magnetic Theory
The experimental laws of electromagnetic theory are summed up by the Max
well equations. In 1865, after becoming acquainted with the experimental results
of his fellow Englishman Faraday, Maxwell gave the electromagnetic theory a
complete mathematical form. We will present speciﬁc parts of the Maxwell
equations: Ampere’s law, Faraday’s law, and Gauss’s law, which together with
Lenz’s law are the basis of magnetic circuit analysis. These are the laws that are
useful in the design of magnetic components for power electronics.
1.1.1 Ampere’s Law and Magnetomotive Force
When an electrical conductor carries current, a magnetic ﬁeld is induced
around the conductor, as shown in Fig. 1.1. The induced magnetic ﬁeld is
characterized by its magnetic ﬁeld intensity H. The direction of the magnetic
ﬁeld intensity can be found by the socalled thumb rule, according to which,
if the conductor is held with the right hand and the thumb indicates the
current, the ﬁngers indicate the direction of the magnetic ﬁeld.
The magnetic ﬁeld intensity H is deﬁned by Ampere’s law. According to
Ampere’s law the integral of H [A/m] around a closed path is equal to the
total current passing through the interior of the path (note that a line above
a quantity denotes that it is a vector):
(1.1)Hl JS⋅= ⋅
∫∫
dd
Sl
DK4141_C01.fm Page 1 Tuesday, January 18, 2005 11:10 AM
Copyright 2005 by Taylor & Francis Group, LLCCopyright 2005 by Taylor & Francis Group, LLC
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