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Leche 19
Multiples + charge distabuhons
Gusida a gerwal chase. Aismbuhos om Wht hve is bebe
pomhue + negahve charge present, fol exomple we can magus a spkve
ose upper boll pombe and lwer iff regaug , Ata qreok
stance. fran tie Sphae , tHe spoe
will Gppeat to be heubkad and we expect
Re tot tea Add will aproadk o-
pest = Cs However, as one. cpproackes Kip s Sphere
clos ve we wall rdreg tat the ovine +
ae ke negahve charges are ot Ai Meent
locakans . Mowe Lea Splut , we
Will be closes te Hee posibve chage tan ta vegahve chaage
ard roe will cotanly be a net Feld Our ain is to deleracine
approxmabons io His tel and ā ascartaar
~ Feld iu fear, intermediate + fy ranges
~ tale ot which held ceceases os one reads Fran
he cage. dismlouhan
in genaral fe Fld ot anu, Dart con he determined most
corseruenttas Tae Hue potorbal, The exoct expresnan is deterred
vio.
\
Free] || POL? oe snet a dota
But we can alo see that
Ta xa
ve {IFl =1TT
aa
Sy ctartte2Ple
4
2 Vir er'reesy!
whoe Ā„' ig Ma are behwern PF andt!
So tie petental con be expessed as a senes valle
Ā¢ L
cue detkeuting powers aA F \
{
Hye. + | (08) or
| Ve) | s ae dt
+ me { ptr.eye) reosĀ„' A!
ao | pregā) rs [scosty'ā] dt!
ps
lig called ey multipdle expansion ot V. for a
chong distbubar ot nile extent ile successive tome weld
small + smaller coumbuhass
Monopole term
āTwwe ss one tom at is always StraighHowaad to
Comp ueā
7 (pire) de! >
whoe Q is tie net chorge ix Re cishouhon
VVovon (F) = _ + {p(Pacā
ail, 1
o a
=D N pon @) = 4leet
This is exachy ihe potential dy a pout charge locahed ad
tba ign wi, total charge Q
Eyorple Cwside a s phot ual. uni born clistibuhan, of pesihue
clarge + Q, on Hee upper Iualf ond anilorm cash bubs
-4, on he wer ball
We monopdle tom in tie poknbal ss
VVonon [?) = ās 1 = Oo
4Mbn F
Dipde feta
āTeo stead tem iSĀ°
3 oo ā
Vaup ) = 416. 6? [pera e'coow at!
and it clearly secles aS Fa āTiss celled the dipde
tou.
Exomple: For He sphare , dekernure Le dupdla coumiboucign fe
* te pdiarhal at paat x,
Loe. ye! cr
yal
āa
[ues :
Example. Delernine Osa dipela momen Se tea preriaus sphocd
Aishnbubaa:
Fit fy he upper halt dea dipdla mower! is oriented
(A alovg 43
Second for Keo lower half Be dipdle nomart is idenkead
+ onenkech along Ā®
So we awd
ge ax | plac
upper half
anh we Only resto find He ~ Component
= 4
Bo ped
pes BH + 2 | BP Gp Aeā
upper
=> Paz 2 | | (> rieoseā ri? sine" drāda' dgā
OO d:o +0
ul
2
= Zron x 34 Bh | coseāmes do!
aie Fe!
6-0
3 2 WW
848 J sia! 7
2 2 a
= 348
4
TT a _ Q zg
[aus Pr LE ad we can canly
dttormma VP) oF any pant
i 1 348 9f