E磁场对电流的作用.pptVIP

Chapter 8 Magnetic Force on Currents,1 Magnetic force on currents Amperes law,2 Magnetic field acts on a loop of wire,3 The work of magnetic force,4 Lorentz force,5 Charged particle moving in electric and magnetic field,6 Hall effect,1 Magnetic force on current Amperes law,1 Experiment 实验现象,A current-carrying wire in a magnetic field experience a force：,If wire is perpendicular to B，the force：F = IBL；,If wire is parallel to B，the force： F = 0；,If the angle between wire and B is, the force: F = IBLsin,Force direction is determined by left hand rule.,2 Amperes law,Magnitude：,Direction：,Force on total current:,3 Examples,Ex 1 determine the force between two parallel straight wires I1，I2，0，a,a,0,I1,I2,The field by wire(I1) at wire(I2):,Magnetic force on current element,Direction as shown in Fig,The force per unit length wire,取a=1m, f=210-7 N/m, I=1A,Parallel wires carrying current in the same direction attract one another,Ex 2 determine the force on a semicircular section of wire of radius R carrying a current I in a magnetic field.,Discuss,(1) The force on rigid circular wire,Corollary: 任一段弯曲载流导线在均匀磁场中所受的磁场作用力，等于从起点到终点连接的直导线通过相同的电流时所受的作用力。,(2) 刚性1/4 圆线圈受力,(3) 连接两端点的直线电流受力,方向: 与x轴夹角/4,Ex 3 Two current-carrying wires is shown in Fig (MN is coplanar with wire I1). Calculate the force on wire MN.,Magnetic force on current element I2dl：,Magnetic force on MN:,The field by current I1 at current I2:,Direction down into page,Direction: as shown in the Fig,2 Magnetic field acts on a loop of wire,a,b,c,d,ad=bc=l1,ab=cd=l2,Result：A current-carrying loop in a magnetic field experiences a torque,bc：,downwards,da：,upwards,ab：,a(b),d(c),Direction as shown in Fig,cd：,equal and opposite, but they do not act along the same line, so they create a torque(力矩),Torque,MIBl1l2cos =IBS cos,I,I,Note,(1) The magnetic torque,(2) Extremum of magnetic torque,=/2：M=Mmax, =0：M=0,Stable equilibrium, =: M=0,Unstable equilibrium,(3) Carrying current loop in uniform magnetic field,The force on the loop of uniform magnetic field is zero.,The torque on the loop of uniform magnetic field is not zero.,Appendix:,(1) A current loop of any shape,Although the equation is arrived for the special case of a rectangular loop, the relation can be generalized to a current loop of any shape by approximating the loop as closely as desired by a number of rectangular loop each having sides parallel and perpendicular to the magnetic field.,(2) A current loop in a non-uniform magnetic field,The force on the loop of non-uniform magnetic field is not zero. The torque on the loop of non-uniform magnetic field is not zero. 线圈既受力的作用，又受力矩的作用，此时线圈除转动外，还有平动。,Ex A disk of radius R has a constant surface charge density , which distributed over the disk. It is shown in the Fig. Please prove the magnetic torque on the disk is:,A ring of radius r and width dr carries a charge element,Current:,dI=dq/T= 2rdr /2= rdr ,The magnetic moment of ring:,dPm=SdI= r3dr,Torque:,dq=2rdr,dr r,3 The work of magnetic force,1 The work of magnetic force: a wire moved in an uniform magnetic field,Force :,Magnitude: F=BIl,Moving a distance aa , the work of F：,A=Faa= BIl aa,Before moving：magnetic flux， 0=Blad,After moving： magnetic flux, =Blad,The work of magnetic force is equal to current I times the increment of magnetic flux .,Direction: towards the right,2 The work of magnetic torque rotated a loop,As shown in Fig，when loop rotates a angle , the work of magnetic torque :,The work of magnetic torque is equal to current I times the increment of magnetic flux .,Conclusion ：The work of magnetic force:,The negative sign means that the positive work of magnetic torque decrease the angle 负号表示磁力矩做正功使减小,4 Lorentz force,1 Lorentz force,2 The characteristics of Lorentz force,(1),The force is perpendicular to both,The work done on a moving particle is zero.,(2),Magnetic force acts on moving charges only.,(3),Up out of page,Down into page,3 The moving charged particle in magnetic field,(1),Uniform rectilinear motion,(2),Uniform speed circular motion,R is determined by the momentum and charge of the particle and by the strength of magnetic field,Applying Newtons second law:,T( )dose not depend on the speed of the particle nor on the radius R,(3),Particle trackhelix line,螺距,与,无关,磁聚焦,从同一点以很接近的速率v射出的很窄的一束带电粒子流，若与B夹角很小， v|近似相等，螺距h近似相等，经h后重聚。,Example A positive particle charged q with speed v goes into an uniform magnetic field,(1) what is its track？,The direction of Lorentz force is perpendicular to direction of the velocity, the particle does uniform circular motion,Lorentz force is centripetal force here.,(2) If another particle with speed 2v goes into B at same point, radius R？If they start at the same time , will they return to this point at the same time?,Starting at same time and same point, they must meet at same time and same point.,5 Particle moving in electric and magnetic field,1 Particle moving in electric and magnetic field,Electric force:,Magnetic force:,The total force on a moving charged particle,匀强电场中,匀强磁场中,2 Application (利用电磁场控制带电粒子的运动) (1) Mass spectrograph 质谱仪 To measure the masses of isotopes (2) Cyclotron 回旋加速器 To accelerate particles in circles 获得高速粒子； (3) Magnetic focusing, magnetic lens 磁聚焦, 磁透镜 Magnetic focusing 磁聚焦: 从同一点以很接近的速率v射出的很窄的一束带电粒子流，若与B夹角很小， v|近似相等，螺距h近似相等，经h后重聚。 magnetic lens磁透镜: 短线圈产生的非均匀磁场的磁聚焦作用， 在电子显微镜中起了与光学仪器中的类似透镜的作用。,6 Hall effect,将一块导体板放在垂直于它的磁场中，当有电流通过导体板时，则在导体板的AA两侧就会产生电压U，这种现象叫做霍耳效应。,若导体板宽为a，厚为b，在磁场不太强时，电位差UH与通过导体的电流强度和磁感应强度B成正比，而与极板的厚度b反比：,霍耳电势差,k：Hall coefficient,Related to material only,理论推导：,q， v，n,运动电子受力：fm= qvB,-,+,电场E，电位差UH，,fm=fe：,电力fe =qE=qUH/a,(1) k与运动电荷的浓度有关(反比）。因此, 通过霍耳系数的测量, 可以确定导体内的载流子的浓度n。 半导体中载流子的浓度，远比金属中载流子的浓度小，所以半导体的霍耳系数比金属的大得多，且半导体内的载流子浓度受温度、杂质以及其他因素的影响很大。因此，霍耳效应为研究半导体载流子的浓度的变化提供了重要的方法。,(2) k与电荷的正负有关，电压U也与载流子的正负号有关。半导体中，n型半导体，载流子为电子，带负电，p型半导体的载流子为空穴，带正电。所以根据霍耳效应系数的正负亦可判断半导体的类型。,(3) 应用：利用半导体的霍耳效应制成的器件称霍耳元件, 在科学技术中有广泛的应用，如测量磁感应强度,测量直流或交流电流,转换信号;也可用于计算机中的计算元件等。,说明：,Ex 1 质谱仪(mass spectrograph):离子源P所产生的离子，经过狭缝S1和S2之间的电场加速后射入滤速器，滤速器中的电场强度E和磁感应强度B相互垂直，且都垂直于离子速度。通过滤速器的离子进入均匀磁场B0中，它们沿着半圆周运动而达到记录它们的照相底片上形成谱线。若测得谱线A到入口处S0的距离为x，试证明与谱线相应的离子的质量为：m=qB0Bx/2E,证明,(1) 滤速器,(2) 质谱分析,