3.1 Magnetic Fields. Oersted and Ampere

Transcription

1 3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field, H e) emnent nd induced M (hysteesis) Oested nd Ampee The ide tht the Eth hd some popety tht mde lodestone (mgnetic) neees lign in N-S diection if the oot of the concept of mgnetic foce field. Oested found tht wie cying cuent lso ffected compss neee nd so estlished tht it is chges in motion tht cete the mgnetic foce field. Actully the fct is tht chges in motion poduce foce on othe chges in motion nd we descie this phenomenon y intoducing the concept of mgnetic field. Ampee fomulted the ide of the foce field when he found tht thee ws foce ceted etween two cuent cying wies: -1-

2 Foce / unit length = II k In SI units, k = 0 / whee 0 = Lte this ws genelized so the foce could e clculted etween two cuent cying cicuits nd. F 0 II 4 1 The definition of mgnetic induction, B If we think of this foce s something hppening to cicuit cused y the totl effect of cicuit, we could ewite the expession fo F s F I 0 I

3 The tem in sque ckets is now popety of ; it is something ceted y cicuit which intects with the cuent in cicuit to poduce the foce on. It is defined s 'field' nd clled the mgnetic induction B. In S.I units, B is Tesl (T). In c.g.s units, B is in Guss (1.0 T = 10 4 guss). [In mny mgnetic suveys c.g.s unit clled the gmm () is used. 1.0 = 10-5 guss = 10-9 T (1.0 nt)]. The foce on n element of cuent then hs the fom: df I B nd if thee is cuent density, J, i.e. volume distiution of cuent, the expession fo B ecomes: 0 J B dv 4 V 1 (3.1.1) This simple fomul fo B ws deived y Biot nd Svt. The diection of the field follows the ight hnd ule - thum of ight hnd in diection of cuent then finges point in diection of B. Fom these definitions nd it of potentil theoy, we cn find the field fom smll loop of wie of dius cying cuent I fom: -3-

4 0 1 B m 4 (3.1.) o, expnded whee 0 ( I) 0 ( I) B cos sin (3.1.3) m I IA This smll loop of cuent is clled mgnetic dipole nd m is clled the dipole moment of the loop. nd e unit vectos in the dil nd diections espectively. If you plot the field lines fom such dipole souce you get: -4-

5 Mgnetic fields in mtte In simplistic clssicl view, ech tom of mtte, suounded y its shell of electons, looks like smll loop of cuent nd so hs mgnetic moment. If the toms e ndomly oiented, the net moment is zeo. If the toms line up, thee will e net moment, M, due to finite loop of mgnetiztion cuent I m s shown in the sketch: M = I m A Rigoously, the moment is computed fo cuents flowing ound volume V nd the mgnetiztion M is the moment pe unit volume. The individul loops my e lined up y n extenl field (like compss neee) - this is pmgnetism. They my e lined up opposite to the inducing field - dimgnetism. They my spontneously line up in smll goups clled domins - feomgnetism. The domins in tun my e lined up y n extenl field. In typicl minels the pmgnetic effect is dominnt ut wek. Minels contining ion, pticully mgnetite Fe 3 0 4, e stongly feomgnetic nd ccount fo the -5-

6 mgnetiztion encounteed in ocks. When thee is mgnetiztion, thee is n dditionl cuent I m, o cuent density J m, which is dded to ny conventionl cuent tht might e pesent. In feomgnetic mteils the mgnetiztion M is ceted y the ppliction of mgnetic field -- n pplied field cuses the domin mgnetiztions to line up. This dds mgnetiztion cuent J m, to ny othe cuent, J, tht might hve een thee so B is now function of J nd J m. 0 J Jm B 1 dv 4 With it of vecto clculus we cn show fom (1) tht B 0 J (3.1.4) nd with mgnetiztion V B J 0 J m nd with simil ppoch to tht used in defining J m nd M we find M (3.1.5) J m nd comining with (4) we get B M J 0 The quntity, B/ 0 - M, whose cul is the 'fee' cuent density is defined s H - the mgnetic field intensity. B H 0 M nd so B = 0 ( H + M ) ( H nd M hve the sme units) Fo histoicl esons the sttement tht the induced mgnetiztion depends on the field hs een witten. -6-

7 M = m H whee m is the mgnetic susceptiility. Becuse M nd H e in the sme units (Amp/m) m is dimensionless ut, e ceful, m SI units = 4 m cgs units Thee is one moe definition to complete this summy desciption of mgnetic field. B = 0 ( H + M ) = 0 ( H + m H ) = 0 ( 1 + m )H so B = H nd is the mgnetic pemeility. The eltionship etween M nd H is complex nd nonline nd is descied y hysteesis cuve, viz: -7-