医学物理学第十四周周三物理のchapter9EM

1、1Chapter 9 Electricity and MagnetismIso_electro_focusing or Immobilized pH gradient SDS聚丙烯酰胺凝胶电泳聚丙烯酰胺凝胶电泳 27.1 Electrostatic field Electric charge (unit)Electron charge = - eProton charge = + e1 C (Coulomb) = 6.24 1018 e1 A (Ampere) = 1 C s-13 Electric field intensity20020000411rrqrrqqkqqFE Superpos

2、ition of Electric field intensities (group of charges)iiEFFqqFE.12100 0 ：vacuum permittivity (真空电容率真空电容率)4 Electric potential energy (电势能电势能)aaaarqql dEql dFW00041 Electric potentialaaaarql dEqqqWV0000411iaiiaiaVl dEVWa = - e Va for electrons5 Electric dipole (偶极子偶极子) Electric dipole momentl qp6 The

3、 electric potential of an electric dipole (偶极子的电势偶极子的电势)210122010214)(44rrrrqrqrqVVVlr cos12lrr221rrr2020cos41cos4rprlqV r2r1l-q+qrr2 - r1aThe electric potential of an electric dipole changes with positions. 7 The dielectrics (电介质电介质)The dielectrics can be solid or fluid. Generally, they are insulat

4、ors (10 /cm) Non-polar molecules like He, H2, N2 Positive and negative charges overlapNo Eelectric Epolar molecules like H2O, CO, SO2 Positive and negative charges do not overlapNo Eelectric E8 Electric field in dielectrics+ - E0Ep00EEEEp01EEr r ：relative permittivity (相相对电容率对电容率)r0 is permittivity

5、of a dielectric （介电常数）（介电常数）9The capacitance C is defined as: Capacitor (电容器电容器) and Capacitance abbaUQVVQC( C V-1)10 bio-membrane and bio-electricitySemi-permeable“+” denotes “K+” (potassium)“-” denotes “Cl-” (chlorine)Experiments show that most cell membranes have membrane potentials (膜电位膜电位). Cel

6、l membranes are Semi-permeableConcentration of KCl: C1 C2Potassium chloride (KCl) 11V2V1 Nernst equation (能斯特方程）能斯特方程）Based on Boltzmann energy distribution law, the density kTEpenn0n1 n2C1 C2V1? V22211,ZeVEZeVEppkTZeVenn101kTZeVenn202V2V1 Semi-permeable, let positive ions pass1221VV kTVVZeenn)(2121

7、Take natural logarithm on both sideskTZekTVVZenn)(ln2121Where 13As n C, we have n1/n2 = C1/C221lnCCZekTV2V1 For C1 C2, ln(C1/C2) 0, 0, therefore, V1 V2 as shown in Fig. 15 Applications of Nernst equation: (1) Resting potential of cells (静息电位静息电位)(ln7 .26ln2121mVCCCCZekTFor T = 273+37=310K, k = 1.381

8、10-23J K-1, Z=1, e = 1.610-19C, note: Vq (J) J/C (Volt)For cells in human body, K+, Na+ and Cl- can go through neuro-cellular membrane but other ions cannot. 16Example: nerve cell (neuron). There are K+, Na+, Cl- and other ions in the nerve cells. Their concentrations are listed as follows:ionsInsid

9、e cell Ci Outside cell Co (mol.m-3)Na+ 10142K+141 5Cl- 4100A-147 4717Experiment shows that the resting potential for nerve cell is )(86)(mVVVexUoutinioUsing Nernst equation, we have:)(8 .7014210ln7 .26)(mVNUaio)(2 .895141ln7 .26)(mVKUio)(9 .851004ln7 .26)(mVClUio18Cl-:Uio UexK+: Uio Uex= -3mVNa+, K+

10、 pump Moving by C(浓度浓度)Moving by EP(电势电势) Inside celloutside cell4100141514210Na+: Uio Uex = 157mV 由于由于K+离子没有达到它的浓度扩离子没有达到它的浓度扩散电势差，仍有少量散电势差，仍有少量K+由内向外由内向外.Na+离子应该形成内高外低的电势离子应该形成内高外低的电势差，但静息电位却是外高内低。这差，但静息电位却是外高内低。这使得不论膜电势差引起的还是浓度使得不论膜电势差引起的还是浓度差应该引起的扩散都使得差应该引起的扩散都使得Na离子离子有从外向内的强大运动趋势。但静有从外向内的强大运动趋势

11、。但静息膜对息膜对Na不具有通透性！不具有通透性！19 Applications of Nernst equation: (2) Action potential (动作电位动作电位) of cellsRemember：Na+ have great tendPolarized cell (resting status)When cells are stimulated, cellular membrane becomes permeable to Na+ suddenly.Under both the actions of electric potential and concentratio

12、n gradient, Na+ ions pour into the inner cells and make inside potential increase. 20Resting potentialAction potentialdepolarizedV(mV)t(ms)-5050Na+ inner cellP: -86 60 (mV)Na+: ratio Cin/Cout 100000/15Then, cellular membrane becomes high permeable to K+ suddenly and potential is quickly fro

13、m 60 to -100mV. And then pumps of Na+ and K+ work and (10ms)21 Cardio-electric knowledgeCardio-muscle cardio-muscle cellsThe rhymed motion of heart results from the propagation of the electric signal in cardio muscle fibre.22 Cardio muscle cellsIn its stimulated process, (a)(b)(e)(d)(c)(a) Polarizat

14、ion (b) de-polarization(c) 除极结束除极结束(通透性通透性)(d) re-polarization(e) polarization 除极和复极的过程，就是心电偶的形成和除极和复极的过程，就是心电偶的形成和消失的过程，对外显示周期性电性。消失的过程，对外显示周期性电性。23Cardio-electric dipole (心电偶心电偶) ：At different positions, it forms different potential. Cardio muscle dipolexoyz),(tzyxPTwinkling electric-cardio-vector

15、 (瞬时心瞬时心电向量电向量) Spatial electric-cardio-vector loop (空间心电向量环）空间心电向量环） 24 Electro-cardiogram 心脏电场空间心脏电场空间向量的周期性。向量的周期性。人体表面两点人体表面两点间的电位（可间的电位（可正可负）的周正可负）的周期性变化图。期性变化图。25心电图导联心电图导联(electrocardiogram lead) http:/ lead or bipolar lead (测量两点相对电压测量两点相对电压)Single lead (测量某点的电位：测量某点的电位：T点电位为零点电位为零) I1 =I2 +

16、I3030201RIVVRIVVRIVVTFTRLTVLVRVF R0R0R0I1I3I2VT26FRLTVVVV312cos41rpVUsing the potential formula of a dipole 120 120 VLVFVRTaking L = , then R = + 120 , F = + 240 ; we have VT = 0.0240cos120coscos412rpV27Electrocardiograph (心电图机心电图机) Three Standard leads I: left hand (+) right hand (-) II: left foot

17、(+) right hand (-)III: left foot (+) left hand (-) Three pressurized (加压加压) single-leads aVR: Right hand (+), LH & LF (-); aVL: Left hand (+), RH & LF (-); aVF: Left Foot (+), RH & LH (-) 28 Six kinds of anterior electrocardiographic leads (六种胸六种胸前导联前导联)T (left hand, right hand and left

18、foot ) (-) V1,V2,V3,V4,V5,V6 (+ individually)Continuous electrocardiograph, kinetocardiogram (心动图心动图), Doctor analysis, computer analysis, 29 Electrophoresis (电泳电泳)The motion of charged particles in an electric field is called electrophoresis. These particles can be cells, virus globulin (球蛋球蛋白白) mo

19、lecules or other particles. Principles: spherical particle, radius r, moving in an electric field E and a fluid with viscous coefficient EqF1vrF62vFF21Mobility (迁移率迁移率)/()/(/LUtLEvd30Different particles have different mobility, so they can be divided by electrophoresis. Sample pointFilter paperPaper

20、 electrophoresis31Iso_electro_focusing or Immobilized pH gradientSDS-PAGE: sodium dodecyl sulfate poly-acrylamide gel electrophoresis SDS-PAGE: 十二烷基硫酸钠十二烷基硫酸钠-聚丙烯酰胺凝胶电泳聚丙烯酰胺凝胶电泳 32毛细管电毛细管电泳仪的基泳仪的基本结构本结构 (The basic structures of capillary electro-phoresis) 33根据物质的荷根据物质的荷/质比质比差异来进行分离，差异来进行分离，比值愈大比值愈大,

21、跑得愈快。跑得愈快。 Electro-osmotic flow (电渗流：液体在毛细电渗流：液体在毛细管内周围形成带正电管内周围形成带正电荷层，其整体向负极荷层，其整体向负极移动的现象移动的现象)eojepjjvvvj = 1， 2， 34(1) Magnetic induction (磁感应强度磁感应强度) B Magnetic fieldBvEqFsinqvBFmagLorentz forceqvFBmMagnetic induction is defined as the maximum force suffered by unit charge and unit speed (单位单位电荷、单位速度所受的最大力电荷、单位速度所受的最大力)FvFv35(2) Hall effect (霍尔效应霍尔效应) electrical current conductor magnetic field0BvqEqvBE dIBKVVUbaabEFmFevIahbV