Electrostatic/magnetostatic forces

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1 Eecsc/gnesc ces spes ppc: eneg e ec eneg ce (vec) ve (vec) en ( eneg ) ( snce) ne s cn gve e O ce (n pessue) u cn en snge sp cne s pe e ce spe epe: pe pes eecsc: ppe vge gnesc: cuen I Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn

2 Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn e pe cpcs ee e es e un, nge es e s ce equn s un usng e sp ce s cve beeen pes cp C U cp U z pe C E Q Q -Q E /

3 e spceen cnse cse ee ne pe s spce snce e pe gnng nge es C ( ) U cp C ( ) U cp > < 0 0 z ce s nep spceen eveses sgn 0 esng ce cenes e pes Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn

4 e spceen eecc sb cnse cse ee eecc sb ( ckness ) s spce snce e pes gnng nge es C ( ) [ ( ) ] Ucp > [ ] ( 0) z ce s nep spceen s ze 0 ce pus sb n egn beeen e pes Den. Nekk 00, s upe Mc 9, 00 4 Dep. ECE, Unv. es usn

5 e spceen ec sb cnse cse ee BISED ec sb s spce snce e pes gnng nge es C C ( ) egn egn B z Ucp > ne ee s NO ne ce n e ecn! ( 0) Den. Nekk 00, s upe Mc 9, 00 5 Dep. ECE, Unv. es usn

6 e spceen ec sb cnse cse ee ng ec sb s spce snce e pes C gnng nge es ( ) egn egn B C B [ ( ) ] z C ( ) [ ( ) ] Den. Nekk 00, s upe Mc 9, 00 6 Dep. ECE, Unv. es usn

7 Den. Nekk 00, s upe Mc 9, 00 7 Dep. ECE, Unv. es usn e spceen ec sb cnse cse ee ec sb s spce snce e pes gnng nge es 0 C U cp > z egn egn B C [ ] C

8 Den. Nekk 00, s upe Mc 9, 00 8 Dep. ECE, Unv. es usn Cpsn bs scees unbse e sb ce < bse e sb n ce n ecn (n bsence nge es) ce s ze nce sb s u beeen e pes z z

9 Eecsc ecnc ce bnce ssue ne pe e, e cnnece spng ce bnce ( ) { cp k k spng ( ) use nze spceen k ( ) z spng E / 4 4 k444 nze ce cp cubc, sve pc Den. Nekk 00, s upe Mc 9, 00 9 Dep. ECE, Unv. es usn

10 Eecsc ecnc ce bnce bvus pbe ce spng s k, bu eec s ese bun n : < ( ) ( ) cp > k{ spng k z spng E / cp k < Den. Nekk 00, s upe Mc 9, 00 0 Dep. ECE, Unv. es usn

11 Eecsc ecnc ce bnce p vs e n nze ce, nesecn gves / spng k 0.5 E / cp ( ) unsbe s ge e pes cpse! Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn

12 ( ) Eecsc ecnc ce bnce ppe vge ecees se u, e cve ce ecees e esng ce e spng ( ) 0 ( ) ( ) 0 ( ) ( ) 0 unsbe spceen s / n sepn k ( ) k Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn

13 Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn Eecsc spceen cneve cpc e b cneve be n e pe cneve be: suppe ne en n pn ce psn, spceen psn p eecn ( ) ue δ psn > < I E 6 δ I I E 6 p δ δ

14 Eecsc be spceen n nege ge p eecn p 0 6 E I ( ) ec ce pe e sepn s ce δ ue eecsc cn bu be equn e spceen e pn ce ppcn E I s sve s uncn eques sun cubc! e E I Den. Nekk 00, s upe Mc 9, 00 4 Dep. ECE, Unv. es usn

15 Eecsc be spceen n nege ge p eecn p 0 6 E I ( ) seng spe ssue pbc benng be en ce δ ue eecsc cn ( ) p s e eecn e p s p p 6 E I 0 [ ( p ) ] sve pc b ssue vue p nse e neg, en nege, cpe neg ssue vue Den. Nekk 00, s upe Mc 9, 00 5 Dep. ECE, Unv. es usn

16 Den. Nekk 00, s upe Mc 9, 00 6 Dep. ECE, Unv. es usn Eecsc be spceen peeze pbe usng p Y nse neg usng pbc pp: negs: [ ] 0 p Y I E 6 [ ] n 4 [ ] n

17 Den. Nekk 00, s upe Mc 9, 00 7 Dep. ECE, Unv. es usn Eecsc be spceen e negn epce Y p usng nze spceen neg beces n { } p p p p p p p p 4 p n n 4 I E 6 p n 4 n I E 4 4 I E n 4 n

18 Eecsc be spceen sve pc b png vs e sun s bne b png nze ce en n vue e nesecn n 4 n 0. E I unsbe 0.47 E I Den. Nekk 00, s upe Mc 9, 00 8 Dep. ECE, Unv. es usn p

19 Den. Nekk 00, s upe Mc 9, 00 9 Dep. ECE, Unv. es usn epneuc cun use see vue epeue cnge ccpne b pessue n vue cnges R N R N k bu k

20 Den. Nekk 00, s upe Mc 9, 00 0 Dep. ECE, Unv. es usn epneuc cun esung equn spceen s quc sve, usng e nze ce α ze spceen sensv epeue ke α bg (css secn e / ) bg k s eng e k 0 k k k α α α α 4 k α

21 Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn e eecn bp be cnse cneve be e es unequ CE s ssue n bu-n sess, ne en pnne cneve 6 R α α α α α > α > 6 E E E E 4 R α α Kvcs (uns e ng) bb-z

22 Den. Nekk 00, s upe Mc 9, 00 Dep. ECE, Unv. es usn

In order to ensure that an overall development in service by those. of total. rel:rtins lo the wapris are

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