物理专业英语组别：19组专业：物理学姓名：9.5 THE LORENTZ FORCEA charge moving in a magnetic field experiences a force which we shall call magnetic . The force is determined by the chang q,its velocity v ,and the magnetic inductionB at the point where the charge is at the moment of time being considered .The simplest assumption is that the magnitude of the force F is proportional to each of the three quantities q,v,and B .In addition ,F can be expected to depend on the mutual orientation of the vectors v and B .The direction of the vector F should be determined by those of vectors v and B.To”construct”che vector F form the scalar q and the vectors v and B ,let us find the vector of v and B and then multiply then multiply the result obtained by the scalar q.The result is the expressionq[vB (9.31）It has been established experimentally that the force F acting on a charge moving in a magnetic field is determined by the formulaFa=kq[vB] （9.32）Where k is a proportionality constant depending on the choice of the units for the quantities in the formula .It must be borne in mind that the reasoning which led us to expression(9.31)must by no means be considered as the derivation of Eq.(9.32)This reasoning does not have conclusive force .Its aim is to help us memorize Eq(9.32).The correctness of this equation can be established only experimentally .We must note that Eq.(9.32)can be considered as a definition of The magnetic induction B.The unit of magnetic induction B -the tesla-is determined so that the proportionality constant k in Eq.(9.32)equals unity .Hence,In SI units ,this equation becomesF=q[vB] (9.33）The magnitude of the magnetic force isF=qvBsin∂(9.34) Where ∂is the angle between the vectors v and B .It can be seen from Eq.(9.34) that a charge moving along the lines of a magnetic field does not experience the action of a magneticforce .The magnetic force is directed at right angles to the plane containing the vectors v and B.If the charge q is positive ,then direction of the force coincides with that of the vector [vB].Where q is negative ,the directions of the vectors F and [vB] are opposite (Fig.9.6).Since the magnetic force is always directed at right angles to the velocity of a charged particle ,it does no work on the particle .Hence ,we cannot change the energy of a charged particle by acting on it with a constant magnetic field .The force exerted on a charged particle that is simultaneously in an electric and a magnetic field isF=qE+q[vB] (9.35)This expression was obtained from the results of experiments by the Dutch physicist Hendrik Lorentz (1853~1928)and is called the Lorentz force.Assume that the charge q is moving with the velocity v parallel to a straight infinite wire along which the current I flows(Fig.9.7).According to Eqs .(9.30)and(9.34),the charge in this case experiences a magnetic force whose magnitude isF=qvB=qv b240I πμ (9.36) Where b is the distance from the charge to the wire .The force is directed toward the wire when charge is positive if the directions of the current and motion of the charge are the same ,and away from the wire if these directions are opposite (see Fig.9.7).When the charge is negative ,the direction of the force is reversed ,the other conditions being equal.Let us consider two like point charges q 1and q2 moving along parallel straight lines with the same velocity v that is much smaller than c (Fig.9.8).When v ∝c,the electric field does not virtually differ form the field of stationary charges (see Sec 。

9.3）.Therefore the magnitude of the electric force F e exerted on the charges can be considered equal toF e ,1=F e ,2=F e =041πε221q rq (9.37) Equations （9.21）and (9.33)give us the following expression for the magnetic force m F exerted on the charges :222102,1,m 4r v q q F F F m m πμ=== (9.38) (the position vector r is perpendicular to v). Let us find the ratio between the magnetic and electric forces It follows from Eqs.(9.37)and(9.38)that22200m cv v Fe F ==με (9.39) [see Eq(9.15)].We have obtained Eq.(9.39) on the assumption that v<<c.This ratio holds ,however,with any v ，s.The forces F e and m F are directed oppositely .Figure 9.8 has been drawn for like and positive charges.For like negative charges, the directions of the forces will remain the same ,while the directions of the electric and magnetic forces will be the reverse of those shown in the figure .Inspection of Eq.（9.39）shows that the magnetic force is weaker than the Coulomb one by a factor equal to the square of ratio of the speed of the charge to that of light.The explanation is that the magnetic interaction between moving charges is a relativistic effect. Magnetism would disappear if the speed of light were infinitely great.9.5 洛伦兹力移动的电荷在磁场中收到磁场力的作用，这种力是由电荷的电量q，速度v和在磁场中所在的位置和该时刻所对应的磁感应强度B决定。