{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

equationsforfinal

# equationsforfinal - x Mow y=psin¢ z=z Ap cos<1 sin<1...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x : Mow, y=psin¢, z=z Ap cos <1) sin <1) O A A45 2 ~sin <15 cos <1) 0 A), AZ 0 0 1 AZ Ax cos <1) sin <1) 0 ‘1 Ap A), = ~sin <1) cos <1) O A}, AZ 0 O 1 AZ 6V 8V 6 VVa—ar —-a‘,+—Xaz 6x 8y az 8V 1 8V VV “ ‘h an _ —‘ 21¢ ﬂ 32 6p 9 6(1) az ‘ 6V 1 VV’" a,.+ avae i 1 6Va¢ 6r 7‘ <96 r sm 6 845 _ Q1Q2 F12 H 471‘80R2 R” “an, x = r sin 6 cos <1), 3 2 r sin 6 sin <15, 2 r cos 6 2 2 x + r = \/x2 + y2 + zz, 6 ~ tan‘1 ) , (1) w taif1 y z x A, sin 6 cos <1) sin 6 sin q) cos 6 A“ A9 = cos 6 cos <1) cos 6 sin q) —sin 6 A), A¢ —sin <1) cos <15 0 AZ Ax —sin 6 cos <1) cos 6 cos <15 —sin <1) A,. A). = sin 6 sin <1) cos 6 sin <1) cos 9b A0 A2 _cos 6 —sin 6 0 A15 V . A 2 an 342 + % 3A 8y 6g 3 1 8A VA=~—m&)~~i Mz 10 6,0 69¢ 82 1 a 1 a , V'A=~~<r2A,)+ -A - 1 LA) V2 <91” rsin6 <96( 681n0)+ rsin6 8g) E = f a 1' h L 471'80R2 R ( inec arge) dS E = 1 ps 3 f S 471'80R2 R (sur ace charge) pp dv E = J 47m R2 aR (volume charge) WE: _ ,12 N 10!9 80 — 8.854 X 10 — 367r F/m k _ 1 : 2 9 X 1091n/F 471—80 01' J=pvll apv V" z _ I at J=UE _ Rzpﬂ S D=8E P = X88013 8 _ 808’ D 2 80E + P 32K + azv + 02V 8x2 (3)72 0Z2 =0 1a<rav>+1gzylazv 0 p ap pap p2 M2 ﬁzz Ja<zav>+ 1 a<.aav>‘ 1 62V 0 ‘ 1‘ 8111 | — 1‘2 (71‘ (7)" / rzsinﬁ 00 ()0 I‘Zsinza a¢2 [d] x dH 2 m : M H = f W4 Rf”? (line mm) 47rR2 4M3 L W HZJK6X% S 471'R2 ng’dl:Icuc HszdvxaR V 4sz V X H = J Mo = 47r X 10‘7 H/m B = MOH . = V - B ‘1“:[3-613 jEBdS 0 S 6A2 6A), . an maﬁa V X A g ‘: a), aZ ax ' aZ 6X )’ + a—AL — BAX] a 6x 6y z 1 M 6A 6A M V x A = — Z a J P * z [93¢ az]ap+[6z 6p]a¢ +l[6(pA¢) _ amp 3 D W) M Z _ 1 6(A¢sin0) _ ﬂ] VXAwrsin6[ 86 0gb 21,. 1 1 3A, a(rA¢) 1 6(rA9) 6A,] + . + rLinf} aqb 8r ]a€ r[ ar 66 34’ (volume cun‘ent) (surface cun‘ent) T=m><B _F=Q(E+u><B) H M 1- Eklemk J” VXM B:“0(H+M) = 1m% H“— Av4>0 AV __ ,l/Ll. : 1 + Xm 2 i M : Xqu B ~ wall #0 = H “ H2 : B111 B2” 1, I (H1 _ H2) X 31112 : K >\ NE” 1 I 1 ngzﬁ W,,=— B‘Hdv=~ H2 1 1 ' 2 2 “ dV BB v — E - d1 — chf: E‘dl= _ m-dS emf— m — (u><B)'dl L S at L L 6B VXE=~E V><H=J+ia12 J 8D I 2 ~ ‘1 dz Differential Form Integral Form Remarks V ‘ D = pv % D * (ITS = J p‘, (1v Gauss’s law S v V ~ B = 0 if B - (ZS = 0 Nonexistence ofisolated S magnetic charge“: V X E = —& jg E - d1 : —3 J B - dS Faraday’s law at I (If 5' 7D ’)D V x H = J + ‘ f; H - (11 = J (J + 57> - (IS Ampére’s circuit law L S V72];Y _ 3,213Y = 0 E(z, r) = Eoewzcosaot — Bz) ax 2 Z - + . E0 _ 'Y JwMa st) H = We dz 008(wt # Bz _ 6,7)331 n . v=a+ﬁ 2 8 a 6 = w [ 1+ [ﬂ] +1] 2 we T~E€_ an E10 712 + 7]} @=EXH E, H1 : 2 ’0 cos 51ZCOS cotay 771 E1 = 2E,~o sin Blz sin wt ax (1:0, ﬁ=wﬂ§o=g C Em<z> = Eoe'“ + Eze“ ﬂ 1 I c, >\ = 27V Ll — __ V #080 5 13(1‘, t) 2 E0 cos(k~r — wt) 1 ak X E : Re[Eoej(k-r—zot)] (UM u=f)\ _ ‘Ellmax ‘Hllmax _ 1 + lF‘ f lEllmin _ IHI‘min * 1 __ IF‘ jw (7+ng ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

equationsforfinal - x Mow y=psin¢ z=z Ap cos<1 sin<1...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online