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Souces Of Mgnetic Fields We lened two wys to clculte Electic Field Coulomb's Foce de 4 E da 1 dq Q enc ˆ ute Foce Clcultion High symmety Wht e the nlogous equtions fo the Mgnetic Field? Winte 4 OSU
Souces Of Mgnetic Fields Now two wys to clculte Mgnetic Field iot-svt Lw I ˆ ute Foce Clcultion 4 Whee unit vecto displcement pointing fom element to the field point P ˆ Ampee s Lw I enc High symmety Winte 4 OSU 3
iot-svt Lw iot-svt Lw; bits nd pieces Mgnetic fields e geneted by moving chge. 4 I 4 1 - pemebility of fee spce 7 ˆ N A ^ I P Winte 4 OSU 4
Concept Checks Winte 4 OSU iot-svt Lw A wie lying in -y plne cies cuent I s shown. Points A,, & C lie in the -y plne s well. Let z-is point out of the sceen y A I z I) Wht is the diection of the mgnetic field contibution t point A due to the segment. 1) + ) - 3) +y 4) -y 5) +z 6) -z C 5
Concept Checks Winte 4 OSU iot-svt Lw A wie lying in -y plne cies cuent I s shown. Points A,, & C lie in the -y plne s well. Let z-is point out of the sceen y A I z I) Wht is the diection of the mgnetic field contibution t point due to the segment. 1) + ) - 3) +y 4) -y 5) +z 6) -z C 6
Concept Checks Winte 4 OSU iot-svt Lw A wie lying in -y plne cies cuent I s shown. Points A,, & C lie in the -y plne s well. Let z-is point out of the sceen y A I z I) Wht is the diection of the mgnetic field contibution t point C due to the segment. 1) + ) - 3) +y 4) -y 5) +z 6) -z C 7
-field of Stight Wie Clculte field t point P R o using iot-svt Lw: I y dy 4π ˆ dy nd R y ( dy)sin θ 4π R R d q θ dy R θ dy y R sinq tn csc q dy Winte 4 OSU 8
-field of Stight Wie Clculte field t point P R o using iot-svt Lw: I y dq dy dy R ( dy)sin θ 4π d q R q dy μ I μ I sin θdq 4πR 4πR πr q cosq Winte 4 OSU 9
-Field of Cicul Loop Cicul loop of dius R cies cuent I. Wht is long the is of the loop: Mgnitude of fom element : = I 4 = I 4 +R q R R q Wht is the diection of the field? Symmety is in -diection. cos q 4π R Winte 4 OSU 1
-Field of Cicul Loop cos q 4π R R R cosq z R R ( Rdq ) 3 4 π ( R ) q R R q μ IR 3 ( R ) At the cente of the loop z = theefoe R Winte 4 OSU 11
-field of Concentic Semicicles Homewok Poblem #9 A cuent I flows in the diection shown. Wht is the Mgnetic Field At point P due to the cuent in the inne semicicle (t = )? 1) μ I 3) ) 4) Winte 4 OSU 5) 4 b P 1
-field of Concentic Semicicles Homewok Poblem #9 A cuent I flows in the diection shown. Wht is the Mgnetic Field At point P due to the cuent in the oute semicicle (t = b)? 1) μ I 3) b b ) 4) b Winte 4 OSU 8b μ Ib b 5) 4 b 4 b P b 13
-field of Concentic Semicicles Homewok Poblem #9 A cuent I flows in the diection b shown. Wht is the Mgnetic Field At point P due to the cuent in the oute semicicle (t = )? 4π R 4πR P diected in the sceen 4R ( ) Rdq Winte 4 OSU Chpte 8 14
Souces Mgnetism in Mtte Obitl mgnetic moment of n electon. Spin mgnetic moment of n electon e Types of Mgnetism Feomgnetic Pmgnetic spin Dimgnetic L Winte 4 OSU 15
Feomgnetism Consists of smll egions (clled domins) whee the mgnetic moments e ligned. With plcing the mteil (domins) n etenl mgnetic field you cn lign the domins. At citicl tempetue clled Cuie Mgnetism in Mtte Tempetue the substnce loses its mgnetiztion nd becomes Pmgnetic. Winte 4 OSU 16
Pmgnetism Mgnetism in Mtte Mgnetic moments within these mteils intect wekly with one nothe. Mgnetic moments will lign in the pesence of n etenl mgnetic field. Cuie s Lw M C T If the mteil is loweed below the Cuie tempetue, it will mintin its mgnetic lignment. Winte 4 OSU 17
Dimgnetism Mgnetism in Mtte Hs no pemnent mgnetic moment. The pesence of n etenl mgnetic field cuses wek opposing mgnetic moment in the mteil Hence the totl field will be less thn the etenl field Dimgnetism is pesent in ll mteils Winte 4 OSU 18