PHY 114 A Geneal Physics II 11 AM-1:15 PM TR Olin 11 Plan fo Lectue 1 Chaptes 3): Souces of Magnetic fields 1. Pemanent magnets.biot-savat Law; magnetic fields fom a cuent-caying wie 3.Ampee Law 4.Magnetic fields in a solenoid 3/6/1 PHY 114 A Sping 1 -- Lectue 1 1
Remembe to send in you chapte eading questions 3/6/1 PHY 114 A Sping 1 -- Lectue 1
Review of magnetic foces: F qv B B d B F I ds B Right hand ule, I ds http://www.fotoseach.com/csp76/k76197/ 3/6/1 PHY 114 A Sping 1 -- Lectue 1 3
Vecto coss poduct kˆ ĵ î ˆi ˆj kˆ ˆj kˆ ˆi kˆ ˆi ˆj ˆj ˆi kˆ 3/6/1 PHY 114 A Sping 1 -- Lectue 1 4
Souces of magnetic fields B Pemanent magnet mateials Fe, Fe O 3, Co, Ni, alloys Intenal atomic level magnet dipole moments Enegy incentive fo neighboing magnetic dipoles to align at tempeatues below Cuie tempeatue. Visualization of intinsic spin magnetic moment of electon. http://littlegeenfootballs.com/weblog/img/bobibutu/11/1/4/magnet.jpg 3/6/1 PHY 114 A Sping 1 -- Lectue 1 5
B B > B >> Pemanent magnets contolled by tempeatue and extenal magnetic fields. 3/6/1 PHY 114 A Sping 1 -- Lectue 1 6
3/6/1 PHY 114 A Sping 1 -- Lectue 1 7 Magnetic fields geneated by moving chage: ' ' ' ') 4 1 ) ) field geneated by chage distibution Electical 3 3 ; d V Q i i i i E ρ πε ρ ' ' ' ') 4 ) ) Magnetic field geneated by cuent distibution 3 3 ; d V Q v i i i i i J B J π
3/6/1 PHY 114 A Sping 1 -- Lectue 1 8 Biot-Savat Law: Units: B T Tesla) J I/aea A/m Constant: pemeability of fee space 4π 1-7 Tm/A 3 3 3 4 ) denotes diection along wie : whee, constant cuent Fo thin wie of ' ' ' ') 4 ) s s s B s J B d I I d π π
Magnetic field poduced by staight wie: B out of sceen) a x min x max B P ) zˆ zˆ 4π I x I 4πa x θ max min θ adx a + x ) cosθ dθ 3/ I B P ) zˆ 1 sinθ 4πa sinθ ) 3/6/1 1 PHY 114 A Sping 1 -- Lectue 1 9
B out of sceen) x min I a x max B Fo P ) x min I zˆ 4πa, sinθ sinθ ) x 1 max : θ 1 B 9 P ) zˆ o, θ I πa 9 o 3/6/1 PHY 114 A Sping 1 -- Lectue 1 1
I 1 I Conside infinitely long) wies. Vote fo the least incoect answe: A. The two wies cancel each othe completely B. The two wies geneate exactly twice the magnet field compaed to a single wie C. The two wies attact each othe. D. The two wies epel each othe. 3/6/1 PHY 114 A Sping 1 -- Lectue 1 11
I 1 I Conside infinitely long) wies. Vote fo the least incoect answe: A. The two wies cancel each othe completely B. The two wies geneate exactly twice the magnet field compaed to a single wie C. The two wies attact each othe. D. The two wies epel each othe. 3/6/1 PHY 114 A Sping 1 -- Lectue 1 1
F I B I 1 I B F wies epel each othe 3/6/1 PHY 114 A Sping 1 -- Lectue 1 13
3/6/1 PHY 114 A Sping 1 -- Lectue 1 14 Magnetic field poduced by wie loop: ) ) ) 3/ 3/ 3/ ˆ 4 ˆ 4 ˆ ) x a Ia x a a I x a d a I P + + + π π θ π π x x x B
Easie way fo situations with high symmety Ampee s Law B ds I in In this case B ds πab I B πa I 3/6/1 PHY 114 A Sping 1 -- Lectue 1 15
Example of Ampee s law: The figue below shows a wie coming out of the sceen. Which of the paths fo has the smallest magnitude? B ds A. a B. b C. c D. d 3/6/1 PHY 114 A Sping 1 -- Lectue 1 16
Magnetic field in a solenoid Ideal solenoid 3/6/1 PHY 114 A Sping 1 -- Lectue 1 17
Magnetic field inside ideal solenoid: Ampee's Law : B ds I in B ds B NI B NI 3/6/1 PHY 114 A Sping 1 -- Lectue 1 18
B NI B 1 T expeimental MRI at FSU) http://www.magnet.fsu.edu/education/tutoials/magnetacademy/mi/images/mi-scanne.jpg 3/6/1 PHY 114 A Sping 1 -- Lectue 1 19
MRI signal detects H nuclei using the magnetic moment of H H. E H B 3/6/1 PHY 114 A Sping 1 -- Lectue 1
Summay: Ampee's law : Integal fom : Diffeential fom : B ds I in B J Gauss's law : Integal fom : Diffeential E fom : ) da E ρ ε Qin ε Note : B ) da B 3/6/1 PHY 114 A Sping 1 -- Lectue 1 1