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1 MIT OpenCourseWre /ESD.013J Electromgnetcs nd Applctons, Fll 005 Plese use the ollowng ctton ormt: Mrkus Zhn, Erch Ippen, nd Dvd Steln, 6.013/ESD.013J Electromgnetcs nd Applctons, Fll 005. (Msschusetts Insttute o Technology: MIT OpenCourseWre). (ccessed MM DD, YYYY). Lcense: Cretve Commons Attrbuton- Noncommercl-Shre Alke. Note: Plese use the ctul e you ccessed ths mterl n your ctton. For more normton bout ctng these mterls or our Terms o Use, vst:

2 6.013, Electromgnetc Felds, Forces, nd Moton Pro. Mrkus Zhn Lecture 18: Felds nd Movng Med November 15,005 I. Ohm s Lw n Movng Med Force on movng chrge: = q( E+ v B) Consder orce on movng chrge n reerence rme (denoted s prme (') rme) movng t chrge velocty v. Then = qe s n the movng rme the reltve velocty s zero. Wth v constnt, nd re nertl rmes (non-ccelertng) so tht: = qe = q E+ v + B E = E+ v + B n prmed rme: J = σe = σ ( E+ v B) I system s chrge neutrl, s s usul cse n MQS systems J = J = σ E+ v B II. Movng Med MQS Problem 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 1 o 0

3 Movng Contour C C d E' dl= S Bnd d v= Bh ξ dξ v= Bh = BhV Sttonry Contour C C' d Edl= B nd= 0 S' B nd n n opposte drectons E'= 0 =E + v B n movng perect conductor v + v B h = 0 v= BhV y 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge o 0

4 III. Frdy s Dsk (Homopolr Genertor) µ 0 N B 0 = s J r J= σ E+ v B E= v B E = ωrb σ πσdr r 0 4 Edl = E dr + Edl = 0 r L 1 3 v r ω 0 r r 0 B0 v r = Er dr = ωrb0 dr = ln 0 πσ dr πσ d 1 ( ) 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 3 o 0

5 = Gω r r ln 0 µ 0N r =, G = 0 πσd s ( ) 7 epresenttve Numbers: copper ( σ ) 6 x10 semen / m, d = 1mm ω = 3600rpm = 10 π rd / s 0 = 10 cm, = 1 cm, B 0 = 1 tesl ωb0 v 0c = ( 0 ) 1.9 V v0c πσd 5 sc = 3x10 mp ln 0 π d 0 φ= 0z= 0r= T= r J B rdrdφdz r _ 0 = r B0 z r dr B _ 0 r 0 = _ = G r z z 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 4 o 0

6 IV. Sel-Excted DC Homopolr Genertor = r d L + ( G ω ) = 0 ; = r + L=L + L [ ω] t =I e 0 G t /L Gω> Sel-Excted r 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 5 o 0

7 V. Sel-Excted AC Homopolr Genertor d1 L + ( Gω ) 1 + Gω = 0 d L + ( Gω) Gω 1 = , Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 6 o 0

8 = I e, = I e st 1 1 Ls + Gω I + GωI = 0 st 1 Gω I + Ls + Gω I =0 1 Ls + Gω + G ω = 0 Ls + G ω = ± jg ω Gω Gω s= ± j L L I1 Gω = = ± j I Ls G ( + ω) Sel Excted: G ω > Oscllton requency: ω =I s =Gω L 0 m 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 7 o 0

9 VI. Sel-Excted Perodc Motor Speed eversls d Gg ωg Gm ωm I + = L L 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 8 o 0

10 dωm J = Gm I st =Ie, ω =We m Gg ωg Gm I I s + W = 0 L L Gm I I + Ws = 0 J st Gg ωg Gm I s s + + = 0 L JL ( G ω ) G ω ( G I ) s= ± L L JL Sel-exctton: G 1 g g g g m g ω > Osclltons s hs n mgnry prt: g ( G I ) ω G m g g > JL L VII. DC Commuttor Mchnes Qus-One Dmensonl Descrpton A. Electrcl Equtons 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 9 o 0

11 C d Edl= S Bnd 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 10 o 0

12 1. Feld Wndng C E dl= v + dl= v + σ A wndng J σ esstnce o eld wndng λ = B nd=l S d v + = L v =L d +. Armture Wndng 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 11 o 0

13 emnder: =q( E+ v B ) =qe' E'=E + v B Tke Sttonry Contour through rmture wndng E=E' v B C Edl= v + E' v B dl b = v + + ωbr z dl ; v= ω Aσ = v + + ω B ln r v B= B r r θ ( χ ) d = B d= L S d d v = + L + Gω G =ln B ( ) r v B. Mechncl Equtons F= J B = B, =FA l= lb _ θ z r θ r w θ Aw r T==lBr N=G d θ J = T =G C. Lner Ampler 1) Open Crcut v = V, =0 = V v =Gω V ) esstvely Loded Armture (DC Genertor) v = L = + GωV 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 1 o 0

14 GωV = ( + ) L Gω V L v = ( + ) L D. DC Motors 1) Shunt Exctton: v = v = v t v = = + Gω t ( ω) G = V V ( Gω) t t =, = V t T=G =G ( Gω) 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 13 o 0

15 ) Seres: = = t ( + + ω) G = v t t v t t = G ( + + ω) v T=G =G G t t ( + + ω) 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 14 o 0

16 VIII. Sel-Excted Mchnes 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 15 o 0

17 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 16 o 0

18 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 17 o 0

19 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 18 o 0

20 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 19 o 0

21 6.013, Electromgnetc Felds, Forces, nd Moton Lecture 18 Pro. Mrkus Zhn Pge 0 o 0

Note: Please use the actual date you accessed this material in your citation.

Note: Please use the actual date you accessed this material in your citation. MIT OpenCourseWare http://ocw.mt.edu 6.13/ESD.13J Electromagnetcs and Applcatons, Fall 5 Please use the followng ctaton format: Markus Zahn, Erch Ippen, and Davd Staeln, 6.13/ESD.13J Electromagnetcs and