CHABAY 0 SHERWOOD
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`C " 3‘22...
`c C 9' {£950.
`
`INTERACTIONS
`
`MATTER
`
`Momentum Dynamics Corporation
`Exhibit 1011
`Page 001
`
`

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`EXLCI'IIVL L‘DI’I’OR .Vttmrt/u/mwn
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`{\SSIS l.-\.\I I:I)|'I'()R .-Il\' Rt'IIII'II/J
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`SENIOR I’R()Dl‘('TI()\ EDITOR If/Izillit‘lli Swim:
`
`.-\RI' I)IRI;'('I'()R Jen] l'ilu
`'I'L".\"I' DESIGN Lauri! lcrtm/I
`SL.\I()R MEDIA LDI'I'OR [humus Kit/em
`
`SI‘iVIOR II.I.l S'I'R.r\'l'l().\ III)I'I’()RS Stu/mutt] .\Iitlmmr,\kl tlntl ."lllltl .llt'lhuru
`
`(‘( )VIiR I\I;\(il"
`
`RHIII ('IIII/HI)‘
`
`(‘o\‘er Description
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`Volume I: Ball-and-spring model ol' a solid
`Volume 3: Magnetic field ot a mmine charge
`
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`Library of Congress Culaluging-in-Publication Data
`
`('Iiaha}. Ruth W.
`Matter & interactions 9' Ruth \\'. Chahay. Bruce A, Sherwood. 7 3rd ed.
`p. cm.
`Includes indes.
`Volume I ISBV ‘WS-tl-Nll—SUMS-J lpl»k.)
`Volume 2 |SB\' II7x-o-47tr5n34h-I Iphk.)
`(‘omplete ISI3.\ "7N-t)»47ll-5tl,‘\47»8 lclothl
`l. I‘ll-\sicsiiI‘uthooks. 2.
`\Iechanicsi’l‘eVIhooks.
`'I'itle: Matter and interactions.
`
`I. Sherwood. Bruce A. |I.'|’it|e. III.
`
`()('Z3.2.('43 ltlll
`5307ch
`
`2110011341; In
`
`Printed in the l'niled States ot America
`
`lows‘7h543‘1
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`Momentum Dynamics Corporation
`Exhibit 1011
`Page 002
`
`

`

`18.9 Magnetic Dipole Moment
`
`725
`
`l-ar ahme the coil in l’igure lh‘Jl. the closer upper part of the coil contributes
`a larger magnetic tield to the lett than does the sliglitl) larthcr a“ a)’ lo“ cr part
`ol the coil to the right. A detailed calculation shims that this is also true a short
`distance abore the coil (l'igure 18.32). (‘ompare the pattern of magnetic lield
`\tith the pattern of t'lt't mt
`tield around an electric dipole.
`
`f"
`If
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`(-
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`Iout ol page
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`If
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`linto page
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`I’igure “1.32 The magnetic tield .il\o\ c
`and l‘t‘lll“ the coil points in the opposite
`clltt'Llliitt l0 llic llcltl illiittli: lllt‘ .t\l\
`
`Magnetic l’ield at Other Locations Outside the Loop
`
`’l'he magnetic held at other locations outside the loop is more dillicult to cal-
`culate anal_\'ticall_\'. but the magnetic tield has a characteristic dipole pattern as
`shown in l‘igut‘e IRS}. u hich is the result ot a computer calculation that added
`up all the contrilmtions ot many short sections ol the loop.
`
`Mr.
`
`A
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`\
`
`o
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`A
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`I
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`I
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`\
`
`l
`I-‘igurr [8.33 'l he magnetic tield ot a
`current loop (“hich lies in [he i: plane.
`\ ie\\cd edge on). .it locations outside the
`loop. in .l plane containing the .i\is ot the
`ltitip
`
`olir'
`
`A Special Right-Hand Rule for (‘urrent Loops
`
`There is another "right-hand rule" that is often used to gel the direction of the
`magnetic tield along the axis of a loop. Let the lingers ol your right hand curl
`around in the direction ot’ the eomentional current. and _\our thumb “‘Ill point
`in the direction ol' the magnetic held at an) location on the axis.
`
`l'r_\' using this right-hand rule to determine the direc-
`QUES'IION
`tion ol the magnetic held at the indicated ohscrtation location in liig
`ure lts'3-l.
`
`l'his right»liand rule
`the magnetic lield points down.
`You should lind that
`should ol' course give the same result as appliing the more general right-hand
`rule to the cross product Al .1 f and adding up the contributions of the \arious
`parts of tltc loop. as called for h) tlte Riot—Smart la“.
`
`1" for two short pieces
`()n the diagram. consider Al— ~
`QUESTION
`of the loop, on opposite sides of the loop. Shou that the two pieces
`together contribute a magnetic field in the do“ nward direction aho\e
`llle loop.
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`18.0 MAGNETICDIPOIJ". MOMENT
`
`CDI
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`Recall the loriiiula tor the electric lield along the a\is ol an electric dipole. at
`a distance r tar li'om the dipole:
`
`Figure INJJ ('tnl the tingeis ot )otii right
`hand in the direction ol the cotncntional
`
`current. and \otn lllllllll‘ \sill point in the
`tliiection ol the magnetic held,
`
`lions ’:
`
`
`3/!
`l
`4.7!“ fl
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`q\. Similarly. in the formula tor the
`\\ here the “electric dipole moment" p
`magnetic licld along the asis ol a current-carrying coil at a distance r far from
`the coil. “1‘ can write this:
`
`nus '5
`'l
`
`[HI 3/1
`4.7 r‘
`
`J
`
`J
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`Figure [8.35 The magnetic dipole
`moment 1)
`is considered to he .i \ectol
`pointing in the direction of the magnetic
`tield along the a\is.
`
`.VI pl.)
`IA. ( If there are N loops. [1
`\\ here the “ magnetic dipole moment" [1
`Here A is the area ot the loop trrlt’3 tor circular loops).
`l‘his formula tor mag-
`netic tield is approutttalel} \alid men it the loop is not circular. The magnetic
`dipole moment [1 is considered to he a sector pointing in the direction ol the
`magnetic field along the axis tl-igure H435). This means that the direction ot
`the magnetic dipole moment can he obtained by curling the lingers of your
`right hand in the direction ot the consentional current. and your thumb points
`in the direction of the magnetic dipole moment.
`
`
`
`Momentum Dynamics Corporation
`Exhibit 1011
`Page 003
`
`