Ch.9. Electromagnetic Induction

Transcription

1 PART Ch.9. Eectomgnetic nuction F. Mutu nuctnce between the Two Cicuits G. Exmpes of nuctnce Ccution H. Enegy Stoe in the Coi. Wok by Eectomgnetic Foce J. Ey Cuent n Skin Effect Yong-Jin Shin, Pofesso of Physics, Chosun Univesity yjshin@chosun.c.k

2 9.F. Mutu nuctnce between the Two Cicuits

3 Vecto Potenti Vecto potenti A Vecto potenti A use fo the theoetic nysis of stey cuent n time-vying cuent t is convenient to obtin the compex mgnetic fie ue to cuent Cuent ensity J in the micoscopic voume v Jv J s s s Vecto potenti A t point P (istnce wy fom the eement on the cuent conuctos) A Mgnetic fux ensity Mgnetic fux ensity t point P by vecto potenti A ota A (cu A)

4 Neumnn s Fomu Vecto potenti vs Mgnetic fux Mgnetic fie cete by the cuent in cose cicuit C Vecto potenti A t point on the cicuit C A C Retionship between mgnetic fux n vecto potenti Mutu nuctnce Neumnn s fomu M s C A s A s s C C C C C C A. Stoke s theoem C C C cos

5 9.G. Exmpes of nuctnce Ccution

6 ) Tooi Soenoi (/) (A) Tooi Coe : vege cicumfeence, cosssection e S, etive pemebiity µ S, cosey woun with N tuns of wie. When cuent [A] fows in tooi N N N(S) with Sef inuctnce? N N N N( S) N N N S S S N S S N S 7 S N S 7 [ H ]

7 ) Tooi Soenoi (/) () Rectngu Tooi Tooi Coi with ectngu coss-section e A n vege ength of cicumfeence is cosey woun with N tuns of wie. (without coe) N N(A) A Sef inuctnce? b with Ni h Ni b Nih N i Nih b n N i N Nh n b N h n b

8 ) nfinite ength Soenoi n ) ( n S n S n n S n n ] [ 7 H n n S S Sef inuctnce fo ength [m]? ] [ 7 H n S n with n(s) Coe : coss-section e S, ius, numbe of tuns pe unit ength n, etive pemebiity µ S When cuent [A] fows in infinitey ong soenoi Sef inuctnce pe unit ength?

9 3) Finite ength Soenoi Coe : coss-section e S, ius, ength [m], tot numbe of tuns N (numbe of tuns pe unit ength n), etive pemebiity µ S N with ( n)( S) n Sef inuctnce? N N S ( n)( S) n Ngok s Coefficient k : (Tbe 9. with / by ekge fux) 7 n n S n S N S N k 7 7 [ H ] [ H ]

10 ) Coxi Cbe (/3) The istibution of cuent in the coxi cbe with ius, b (b > ). Sef inuctnce of coxi cbe is the sum of inuctnce insie n outsie of cyine. () nuctnce t outsie of the cyine ( < < b ) Mgnetic fie intensity H [ A/ m] Mgnetic fux ensity [ Wb / m]

11 Mgnetic fux though the e (ength m, with ) s ) ( Mgnetic fux pe unit ength pssing between two conuctos b b b n Sef inuctnce of oute conucto (# of tuns N=) N b N n (b) nuctnce t insie of the cyine ( < ) Mgnetic fie intensity ' H whee ', with ) Coxi Cbe (/3)

12 v H W W W ), ( v whee Mgnetic enegy pe unit ength insie conucto Sef inuctnce of inne conucto W ] [ 8 H i (c) nuctnce pe unit ength of coxi cbe ] [ 8 og H b i ) Coxi Cbe (3/3)

13 5) Pe Roun Conucting Wie Two conuctos of ius [m] Conucto n b e pce pe to the istnce [m] Wht is the inuctnce pe unit ength of ountip conucting wie ( )? Mgnetic fie intensity ] / [ ) ( m A x x H H H b Mgnetic fux ensity ] / [ ) ( m Wb x x b Mgnetic fux pssing though the point P (e = ength [m] x with x[m]) x x x x s ) ( (/)

14 Mgnetic fux pe unit ength though the e between two conucting wie. [ < x < (-) ] (/) x x x Sef inuctnce ( ) x x n n ) n( n n n s s n n 8 8 ib i i Whee, if you ecognize the inuctnce of inne conucto 5) Pe Roun Conucting Wie

15 9.H. Enegy Stoe in the Coi

16 Enegy Stoe in the Coi Mgnetic-fie enegy Estbishing cuent in n inucto equies n input of enegy, n n inucto cying cuent hs enegy stoe in it. et the cuent t some instnt be i n et its te of chnge be i/t. The votge between the temins n b of the inucto t this instnt is V b =i/t, n the te P t which enegy is being eivee to the inucto (equ to the instntneous powe suppie by the exten souce) is P Vbi The enegy W suppie to the inucto uing n infinitesim time intev t is W Pt i i t ii Thus, the tot enegy W suppie which the cuent inceses fom zeo to fin vue is W W ii

17 Enegy Stoe in the Coi Enegy stoe in the coi Enegy stoe in the unit voume of the coi N H with m J H S W w ] / [ 3 ] [ ] [ H SN with J W ] [ J S N SN SN W ] / [ ] / [ 3 m Wb H with m J H w The Mgnetic cicuit, ength of cicumfeence [m], coss-section e S[m ], pemebiity of coe μ[h/m], n cosey woun with N tuns of wie. Cuent [A] fows in mgnetic cicuit.

18 9.. Wok by Eectomgnetic Foce

19 Wok by Eectomgnetic Foce The mgnetic fux ensity [Wb/m ] is unifom n iecte into the pge, n we move the o(with ength [m]) to the ight t constnt veocity v[m/s] Motion emf : E v Cuent fowing in conucto by eectomotive foce Eectomgnetic foce : F Mechnic enegy W F vt vt Eectic enegy Et vt m W e m Wm W e Mgnetic fux by the psse e of o S vt with S vt Mgnitue of wok by cuent in the mgnetic fie W vt

20 Motion Eectomotive Foce (Ch.9. pt ) Mgnetic fux ensity [ Wb / m ] Chnges in the mgnetic fux in the cose cicuit S vt nuce eectomotive foce (EMF) e( ) v (Diection of emf iecte fom P to Q) t Feming s ight-hn ue e ( v ) vsin

21 Mgnetic Foce on Wies (Cuent ine) The mgnetic foce on the cuent-cying wie in mgnetic fie. The mgnetic foce on the moving chges with in the conucto e tnsmitte to the mtei of the conucto, n the conucto s whoe expeiences foce istibute ong its ength. F q v F Cuent : (Ch.7. pt ) qv Vecto : ong the wie in the iection of the cuent () Mgnetic fie, ength, n foce F vectos fo stight wie cying cuent. (b) Revesing eveses the foce iection (c) Revesing the cuent eveses the foce iection

22 9.J. Ey Cuent & Skin Effect

23 Ey Cuent Chnge of mgnetic fux though the coi Conucting wie moving though mgnetic fie nuces n eectomotive foce (emf) in the coi o wie Coesponing emf equie to cuse inuce cuent. nuce cuent so occus in the met hs nom shpe n size. Mgnetic Fux (incese) nuce Cuent Ey Cuent Met Pte Ey cuent oss : P f e m Eectic equipment (such s tnsfomes n motos) using minte coe me of oe thin stee ptes insute fom ech othe. Reuce the ey cuent

24 Skin effect When iect cuent (DC) fows in the cyinic conucto inuce eectomotive foce is zeo. unifom cuent fows though the conuctos e i t t When n tenting cuent (AC) fows in the cyinic conucto inuce eectomotive foce occus. ( e ) The skin effect is ue to opposing ey cuents inuce by the chnging mgnetic fie esuting fom the tenting cuent. The skin effect cuses the effective esistnce of the conucto to incese t highe fequencies whee the skin epth is sme, thus eucing the effective coss-section of the conucto. Skin epth (o epth of penettion) f [ m] f : ngu fequency of cuent : pemebiity of the conucto ncese AC esistnce ue to the skin effect cn be mitigte by using speciy woven itz wie. : conuctivity of the conucto

25 Pctice Pobem, 5, 6, 9,,, 6, 5, 7 Pevious Tests, 3,, 6, 8,,,, 7,,, 6, 9, 3, 36, 37, 39,, 3, 5 Thnks