Diamagnetism e 1=2 eo 2元 ，me1R2i.=22R2i=e9Ri /0 Angular Momentum [=mRi,x=mR(R)x=mR, (Fxp) 、 2mem e linear momentum L is quantized in units of h=6.62x10-34 joule-sec 2π (Planck's constant) e且- m=2m eh eh≈9.3x10-24amp-m2 2π(2)m。4πme Bohr magneton ms (smallest unit of magnetic moment) Imagine all Bohr magnetons in sphere of radius R aligned.Net magnetic moment is m=me 台aRp Ao Avogadro's number 6.023 x 1026 molecules per kilogram-mole M Total mass molecular weight of sphere For iron:p =7.86 x 103 kg/m3,Mo=56 Figure 9.0.1 (a)Current i in loop of -R radius R gives dipole moment m.(b) 2R Spherical material of radius R has dipole moment approximated as the sum of atomic (a) (b) dipole moments Courtesy of Hermann A.Haus and James R.Melcher.Used with permission. 6.641,Electromagnetic Fields,Forces,and Motion Lecture 8 Prof.Markus Zahn Page 2 of 136.641, Electromagnetic Fields, Forces, and Motion Lecture 8 Prof. Markus Zahn Page 2 of 13 Diamagnetism Angular Momentum ( ) _ __ _ 2 r rz L=mRi v=m R R i i =m R i ee e φ ⎛ ⎞ × ω× ω ⎜ ⎟ ⎝ ⎠ (r p× ) = m 2me e − linear momentum L is quantized in units of h 34 , h = 6.62 x10 joule sec 2 − − π (Planck’s constant) Bohr magneton mB (smallest unit of magnetic moment) Imagine all Bohr magnetons in sphere of radius R aligned. Net magnetic moment is 3 0 B 0 4 A mm R 3 M ⎛ ⎞ = πρ ⎜ ⎟ ⎝ ⎠ Total mass molecular weight of sphere For iron: ρ =7.86 x 103 kg/m3 , M0=56 Courtesy of Hermann A. Haus and James R. Melcher. Used with permission. Avogadro’s number = 6.023 x 1026 molecules per kilogram−mole ω − ω − π π π π ω _ 2 z e e e I= = , m= I R i = 2 2 2 π − ω _ 2 _ 2 z z e R Ri= i 2 ( ) − ≈ − 24 9.3 x10 amp π π 2 e ee e L e h eh m= = = m 2m 2 2 m 4 m