Gauss_Law - ”LL L f f In applying Gausx law 45945 S We...

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Unformatted text preview: ”LL L f . f; In applying Gausx' law 45945 S We decompose P : (Dna + tht) Which {pbdgz cgvbncls : En (gm: Ne can fake Dr) outsidc of ’rhe inkgrql if 3)“ ‘ns constam (as OUH fhe closed Surface. in 0w SimPIQ examplu) \th happens if Dn is not a commmt? Wt men have ’m Comic!” a cli{{cvenh'al Volume. element S +§ : w Aquuz from back 0X A2 P Similavlg 021 J + J ,___ 9.13:1 maul/)2 hth It.“ ‘3 (incl - 33:: exam» y 1‘ I ' 82 hp bottom an BBQ, aDZ _ ___/_ + M + ——- AV — S Since AV- AXAflAY: 99 32"” G) S .- "" : 6V ”’27“ " “V gum Avao M ” avacH‘S cliv b or Y“? - 6V DivLygwce of q Uta-or field 9-6. = 996-6“: / ism [xv-’0 A V The divevqence o( a Uccfvv field A is “36 outflow of fhe {ll/1x {yam a small dated SMYfaa pev unit volume C45 “39 wlume slrm‘nlu fa Zam- EXP'eSSionr {or Divergence I \7-D “- 9331‘ + {DJ-.9 1” 5.2—1}. Carl-char) " ‘ 6} M 3’2} (9 (Q3?) + J— 3qu + 9D: Cfllincln‘ml ’— 1. .___ 9 39 9 act 32 ”D1: Divevgcnce Thaw/cm The clivcvgcnce mm m jm Mew/Ur) if Camj V: cm a general Jiclcl . chfl \Z i} at P (0,0,0) ,{3 x —-x ' ~ —* a *2? a ‘P " C 31011 9x 8 C056] -5 .2 7 D t { &.Dx + 32g + (2L3: > _ _ \3; 55 d2 ”x —-X 7 : ‘" Q S: + e 815, +¢ \7 D (P) ' Z acmanuj {9:2 {waHXM’z Example 7. 'L If 1): ng CLX+X (3.5 C/MZ Evaluql-e boih sidu 939.45: S JO! 0 FataHLIapiPcA X2011 I (5:0)2. I of fhc clt'vergcnze rh-Loyim SW12) Av [armed b5 S . h ‘ Front back ’rvp bornm 1612‘ j ; f? ()m) CIZCIIj 9x J 3 flan} Z 3 Z " 2 6,261 :. S 1 d} # H ‘4 ”1 [w 10 o o o ‘3 : [Aron : {2 o 1’: mm: ow fhm all orhu compcrum‘j .3 0 {Can C(ou show Hm 7] Q-H-S- a 1 Y P fiw") ‘71,“) 2:5 3 z I jq?du_ J I (27 dxdgclg O U 0 2 2 1 ] (33°15 " [3,12] 6 D u ...
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