—aoe
`‘TUeo© 55.
`ce RB2)
`
`SeMATTER A
`
`Momentum Dynamics Corporation
`Exhibit 1011
`Page 001
`
`

`

`EXECUTIVE EDITOR=Stuart Johnson
`
`ASSISTANT EDITOR Aly Rentrop
`ASSOCIATE MARKETING DIRECTOR=Christine Kushner
`SENIOR PRODUCTION EDITOR Elizabeth Swain
`
`ART DIRECTOR|Jeof Vita
`TEXT DESIGN Lauralerardi
`SENIOR MEDIA EDITOR Thomas Kulesa
`
`SENIOR ILLUSTRATION EDITORS Sigmund Malinowski and Anna Melhorn
`
`COVER IMAGE Ruth Chabay
`
`CoverDescription
`
`
`
`
`
`Volume 1: Ball-and-spring model ofa solid
`Volume 2: Magnetic field of a moving charge
`
`This book was set in 10/12 Times Ten Romanin LaTex by Aptara™, Inc. and printed and bound
`by Courier Kendallville.The cover was printed by Courier Kendallville.
`
`This book is printed onacid-free paper.
`
`Copyright © 2011, 2007, 2002 John Wiley & Sons,Inc. All rights reserved.
`
`No part of this publication may be reproduced, storedin a retrieval system or transmittedin any
`form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,
`except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without
`either the prior written permission of the Publisher, or authorization through payment of the
`appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 RosewoodDrive,
`Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission
`shouldbe addressedto the Permissions Department, John Wiley & Sons, Inc., 111 RiverStreet,
`Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website
`http://www.wiley.com/go/permissions.
`
`Evaluation copies are provided to qualified academics andprofessionals for review purposes
`only, for use in their courses during the next academic year. These copies are licensed and may
`not be soldor transferredto a third party. Upon completion ofthe reviewperiod, please return
`the evaluation copy to Wiley. Returninstructions and a free of charge return shipping label are
`available at www.wiley.com/go/returnlabel. Outside of the UnitedStates, please contact your
`local representative.
`
`Library of Congress Cataloging-in-Publication Data
`
`Chabay, Ruth W.
`Matter & interactions / Ruth W. Chabay, Bruce A. Sherwood. —3rded.
`p. cm.
`Includes index.
`Volume 1 ISBN 978-0-470-50345-4 (pbk.)
`Volume 2 ISBN 978-0-470-50346-1 (pbk.)
`Complete ISBN 978-0-470-50347-8 (cloth)
`1. Physics—Textbooks. 2. Mechanics—Textbooks.
`Title: Matter and interactions.
`
`I. Sherwood, Bruce A. II. Title. II.
`
`QC23.2.C43 2011
`530—dec22
`
`2009034010
`
`Printedin the United States ofAmerica
`
`10987654321
`
`
`
`Momentum Dynamics Corporation
`Exhibit 1011
`Page 002
`
`

`

`18.9 Magnetic Dipole Moment
`
`725
`
`Far above the coil in Figure 18.31, the closer upper part ofthe coil contributes
`a larger magnetic field to the left than does the slightly farther away lower part
`of thecoil to the right. A detailed calculation shows that this is also truea short
`distance above the coil (Figure 18.32). Compare the pattern of magnetic field
`with the patternofelectric field around anelectric dipole.
`
`/ out of page
`
`B
`
`/ into page
`
`=B
`
`_
`
`Figure 18.32 The magnetic field above
`andbelow thecoil points in the opposite
`direction to thefield along theaxis.
`
`MagneticField at Other Locations Outside the Loop
`
`The magneticfield at other locations outside the loop is more difficult to cal-
`culate analytically, but the magneticfield has a characteristic dipole pattern as
`shownin Figure 18.33, whichis the result of a computer calculation that added
`upall the contributions of manyshort sections of the loop.
`
`AVA
`
`A
`
`~
`
`—
`
`A
`
`a
`
`A Special Right-Hand Rule for Current Loops
`
`There is another “right-hand rule” that is often used to get the direction ofthe
`magnetic field along the axis of a loop. Let the fingers of your right hand curl
`aroundin the direction of the conventional current, and your thumbwill point
`in the direction of the magneticfield at any location on theaxis.
`
`QUESTION|Tryusing this right-hand rule to determine the direc-
`x
`‘X
`tion of the magnetic field at the indicated observation locationin Fig-
`ure 18.34.
`
`Y
`
`the magnetic field points down. This right-hand rule
`You should find that
`Figure 18.33 The magneticfield of a
`should of course give the same result as applying the moregeneral right-hand
`current loop(whichlies in the xz plane,
`rule to the cross product Al x ? and adding upthe contributions of the various
`viewed edge-on), at locations outside the
`parts of the loop, as called for by the Biot-Savart law.
`loop, in a plane containing the axis of the
`loop
`
`QUESTION|Onthe diagram, consider Al x ? for two short pieces
`of the loop, on opposite sides of the loop. Show that the two pieces
`together contribute a magnetic field in the downward direction above
`the loop.
`
`eB=?
`
`QJ->/
`
`Recall the formula for theelectricfield along the axis of an electric dipole, at
`a distance r far fromthe dipole:
`
`18.9 MAGNETIC DIPOLE MOMENT
`
`Figure 18.34 Curl the fingers of your right
`handin thedirection of the conventional
`
`.
`Exxis ~~
`
`1
`
`2p
`—
`4req v3
`
`current, and your thumb will point in the
`direction of the magneticfield.
`where the “electric dipole moment” p=qs. Similarly, in the formulafor the
`magnetic field along the axis of a current-carrying coil at a distance r far from
`the coil, we can write this:
`
`Baxis ~~
`™
`
`fo 2p
`4x 3
`
`where the “magnetic dipole moment” x=/ A. (If there are N loops, 4=N/A.)
`Here Ais the areaof the loop (7R° for circular loops). This formula for mag-
`=
`=
`neticfield is approximately valid evenif the loopis not circular. The magnetic
`dipole moment ji is consideredto bea vector pointing in the direction of the
`magneticfield along the axis (Figure 18.35). This means that the direction of
`the magnetic dipole moment can be obtained by curling the fingers of your
`right hand in the direction of the conventional current, and your thumbpoints
`in the direction of the magnetic dipole moment.
`
`Figure 18.35 The magnetic dipole
`moment ji
`is consideredto be a vector
`pointing in the direction of the magnetic
`field along theaxis.
`
`
`
`Momentum Dynamics Corporation
`Exhibit 1011
`Page 003
`
`