Electromagnetism PHY 712
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This 2 page Class Notes was uploaded by Miss Lucienne Hamill on Wednesday October 28, 2015. The Class Notes belongs to PHY 712 at Wake Forest University taught by Natalie Holzwarth in Fall. Since its upload, it has received 17 views. For similar materials see /class/230730/phy-712-wake-forest-university in Physics 2 at Wake Forest University.
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Date Created: 10/28/15
February 27 2000 Notes for Lecture 13 Dipole and quadrupole elds The dipole moment is defined by p div2W 1 with the corresponding potential 1 p I I 7 2 I 4W50 7 2 and electrostatic field 1 3fp f39 p 4W 3 E 7 x t r m 3 pa r 3 The last term of the field expression follows from the following derivation We note that Eq is poorly defined 7 gt 0 and consider the value of a small integral of Er about zero For this purpose we are supposing that the dipole p is located at r O In this case we will approximate Er z 0 z ltth Erd3r 531 4 First we note that Erd3r R2 rdn 5 TSR rR This result follows from the Divergence theorm m v Vdsr umvdA 6 In our case this theorem can be used to prove Eq 5 for each cartesian coordinate if we choose V E 5ltIgtr for the x component for example 7 A A 3 A A 3 A A 3 lamp xrSRv xltIgtd wryv yltIgtd rlzFSRV zlt1gtd r which is equal to lt1gtrR2dQ 32 m y my 2 m RltlgtrR2dQi 8 TR r Thus 3 i 3 2 A SREQM r SR VltIgtrd r R rrd9 03g 9 09w 39 d E I IJIJdIJ p I ZHW I 31m UPJJltIgt zH sammaq g1 39bg mm as H lt pm 1 gt twp IJ uopnqmsgp a8qu am sasopua 13qu mp 31 39H sngpm 13qu am pm 1 axqzzmm unmax mug am Imammq aagoqa p 8 lt1 pm gt 30 aggoqa aql 9 09 gnu I ltJ y at 39 IJd1JgP UPJJltIgt zH uogssaxdxa am 0 paman uogmx mug am 30 33ng am pm satx1x3um mm 7 am 5pm g 39bg Hg 3 38th puns on 1218mm mp amnpma am Imqm 1033qu U m ampJ lamp b J 9803 ISWMS mm cu0803 was ISUOQJIHU JEUOUALXRQ ROEJGQdS 30 8mm HE U633 JAA Gq U123 ROGA mm GIQ Rl G30U 081 6AA JltIgt lt 72 7 09117 I Il 09117 2 I I A 01 1 lamp31 amplgt Jd tgp W g I 4 My Map I 4 03 Sugpmam Jd K3 SIXGp a mqg 319 may paugmwmp aq um 1291mm mesrmaap am 31219 3901 am moN
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