Chapter 28 Sources of Magnetic Field


 Theodore Heath
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1 Chpte 8 Souces of Mgnetic Field  Mgnetic Field of Moving Chge  Mgnetic Field of Cuent Element  Mgnetic Field of Stight CuentCying Conducto  Foce Between Pllel Conductos  Mgnetic Field of Cicul Cuent Loop  Ampee s Lw  Applictions of Ampee s Lw  Mgnetic Mteils
2 1. Mgnetic Field of Moving Chge  A chge cetes mgnetic field only when the chge is moving. Souce point: loction of the moving chge. Field point: point P whee we wnt to find the field. Mgnetic field fom point chge moving with constnt speed B q vsinϕ 17 Wb/A m N s /C N/A T m/a (pemebility of vcuum) c (1/ ε ) 1/ speed of light
3 Mgnetic field of point chge moving with constnt velocity B vecto fom souce to field point qv ˆ ˆ / Moving Chge: Mgnetic Field Lines  The mgnetic field lines e cicles centeed on the line of v nd lying in plnes pependicul to tht line.  Diection of field line: ight hnd ule fo + chge point ight thumb in diection of v. You finges cul ound the chge in diection of mgnetic field lines.
4 . Mgnetic Field of Cuent Element  The totl mgnetic field cused by sevel moving chges is the vecto sum of the fields cused by the individul chges. dq nqadl (totl moving chge in volume element dl A) Moving chges in cuent element e equivlent to dq moving with dift velocity. db (I n q v d A) dq v sinϕ n q v Adl sinϕ d d Idl sin ϕ Cuent Element: Vecto Mgnetic Field B Idl ˆ Lw of Biot nd Svt
5 Cuent Element: Mgnetic Field Lines  Field vectos (db) nd mgnetic field lines of cuent element (dl) e like those geneted by + chge dq moving in diection of v dift.  Field lines e cicles in plnes to dl nd centeed on line of dl.
6 3. Mgnetic Field of Stight CuentCying Conducto Idl ˆ B 4 π dl ˆ dl 1 sinϕ dl sin( π ϕ) dl x x + y B I x dy I 3/ ( x + y ) x x + If conductos length >> x B I ) x I B π I π x ( B diection: into the plne of the figue, pependicul to xy plne Field ne long, stight cuentcying conducto
7  Electic field lines dite outwd fom + line chge distibution. They begin nd end t electic chges.  Mgnetic field lines encicle the cuent tht cts s thei souce. They fom closed loops nd neve hve end points. The totl mgnetic flux though ny closed sufce is zeo thee e no isolted mgnetic chges (o mgnetic monopoles) ny mgnetic field line tht entes closed sufce must lso emege fom tht sufce.
8 4. Foce Between Pllel Conductos  Two conductos with cuent in sme diection. Ech conducto lies in B setup by the othe conducto. B geneted by lowe conducto t the position of uppe conducto: I B π F F L I' L B I I' π F I I' LB I' L π Two long pllel cuentcying conductos Foce on uppe conducto is downwd.  Pllel conductos cying cuents in sme diection ttct ech othe. If I hs conty diection they epel ech othe.
9 Mgnetic Foces nd Defining the Ampee  One Ampee is the unvying cuent tht, if pesent in ech of the two pllel conductos of infinite length nd one mete pt in empty spce, cuses ech conducto to expeience foce of exctly x 17 N pe mete of length. 5. Mgnetic Field of Cicul Cuent Loop Idl ˆ B Idl B I dl db 4 π x + ( ) I dl db x db cosθ + ( x + ) ( ) 1/ x θ I dl db y db sin x + x ( x + ) ( ) 1/
10  Rottionl symmety bout x xis no B component pependicul to x. Fo dl on opposite sides of loop, db x e equl in mgnitude nd in sme diection, db y hve sme mgnitude but opposite diection (cncel). B x I dl I dl I 3/ ( ) 3/ 4 ( ) 3/ 4 x + π x + π ( x + ) (π ) I B x + ( x ) 3/ (on the xis of cicul loop)
11 Mgnetic Field on the Axis of Coil NI B x + ( x ) 3/ (on the xis of N cicul loops) NI B x (t the cente, x, of N cicul loops) N I A N I ( π ) B x π + ( x ) 3/ (on the xis of ny numbe of cicul loops)
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