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Electrical MachinesFundamentals

Electrical Machines: Fundamentals 1 Fundamentals 1.1 Maxwell’s Equations 1.1.1 The Maxwell’s Equations in Differential Form The basis for all following considerations are the Maxwell’s equations. In differ- ential form these are (the time-dependent variation of the displacement current D can always be neglected against the current density J for all technical systems re- garded here): 1. Maxwell’s equation G GG dD rotH=+ J ≈ J (1.1) dt 2. Maxwell’s equation dB rotE =− (1.2) dt 3. Maxwell’s equation divB =0 (1.3) 4. Maxwell’s equation divD = ρ (1.4) The material equations are: G G BH = μ (1.5) G G DE =ε (1.6) © Springer-Verlag Berlin Heidelberg 2015 1 D. Gerling, Electrical Machines, Mathematical Engineering, DOI 10.1007/978-3-642-17584-8_1 2 1 Fundamentals G G JE = γ (1.7) The used variables have the following meaning: H the vector field of the magnetic field strength; J the vector field of the electrical current density; D the vector field of the displacement current; E the vector field of the electric field strength; B the vector field of the magnetic flux density; ρ the scalar field of the charge density; μ the scalar field of the permeability (in vacuum or air there is: μ = μ ); http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Electrical MachinesFundamentals

Part of the Mathematical Engineering Book Series (volume 4)
Gerling, Dieter
Electrical Machines — Sep 4, 2014
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35 pages

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2015
ISBN
978-3-642-17583-1
Pages
1 –35
DOI
10.1007/978-3-642-17584-8_1
Publisher site
See Chapter on Publisher Site

Abstract

1 Fundamentals 1.1 Maxwell’s Equations 1.1.1 The Maxwell’s Equations in Differential Form The basis for all following considerations are the Maxwell’s equations. In differ- ential form these are (the time-dependent variation of the displacement current D can always be neglected against the current density J for all technical systems re- garded here): 1. Maxwell’s equation G GG dD rotH=+ J ≈ J (1.1) dt 2. Maxwell’s equation dB rotE =− (1.2) dt 3. Maxwell’s equation divB =0 (1.3) 4. Maxwell’s equation divD = ρ (1.4) The material equations are: G G BH = μ (1.5) G G DE =ε (1.6) © Springer-Verlag Berlin Heidelberg 2015 1 D. Gerling, Electrical Machines, Mathematical Engineering, DOI 10.1007/978-3-642-17584-8_1 2 1 Fundamentals G G JE = γ (1.7) The used variables have the following meaning: H the vector field of the magnetic field strength; J the vector field of the electrical current density; D the vector field of the displacement current; E the vector field of the electric field strength; B the vector field of the magnetic flux density; ρ the scalar field of the charge density; μ the scalar field of the permeability (in vacuum or air there is: μ = μ );

Published: Sep 4, 2014

Keywords: Magnetic Energy; Hysteresis Loss; Iron Loss; Eddy Current Loss; Flux Linkage

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