Field Models in Electricity and Magnetism
Paolo Di Barba • Antonio Savini • Sławomir Wiak
Field Models in Electricity and Magnetism
Paolo Di Barba University of Pavia Dept. Electrical Engineering Via Ferrata, 1 27100 Pavia Italy
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Antonio Savini University of Pavia Dept. Electrical Engineering Via Ferrata, 1 27100 Pavia Italy
Sławomir Wiak Technical University of Lodz Inst. Mechatronics and Information Systems ul. Stefanowskiego 18/22 90-924 Lodz Poland
ISBN 978-1-4020-6842-3
e-ISBN 978-1-4020-6843-0
Library of Congress Control Number: 2008922192 © 2008 Springer Science+Business Media, LLC No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper. 9 8 7 6 5 4 3 2 1 springer.com
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Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Basic Operators and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Vector Fields and Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Definition of a Vector Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Decomposition of a Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Scalar and Vector Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Green’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.6 Green’s Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Electrostatic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Maxwell’s Equations for Electrostatics . . . . . . . . . . . . . . . . . . 2.2.2 Electrostatic Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Electrostatic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Field of a Charged Plane in a Rectangular Domain . . . . . . . . 2.2.5 Field of a Point Charge in a Spherical Domain . . . . . . . . . . . . 2.2.6 Field of a Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.7 Field of a Line Charge in a Cylindrical Domain . . . . . . . . . . . 2.2.8 Field of a Surface Charge on a Sphere . . . . . . . . . . . . . . . . . . . 2.2.9 Energy and Forces in the Electrostatic Field . . . . . . . . . . . . . . 2.2.10 Force between the Plates of a Capacitor . . . . . . . . . . . . . . . . . 2.2.11 Force at the Interface between Two Dielectric Materials . . . . 2.3 Magnetostatic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Maxwell’s Equations for Magnetostatics