Electromagnetic jet propulsion: non-lorentzian forces on currents?
Electromagnetic jet propulsion: non-lorentzian forces on currents?
复制标题
电磁喷射推进：电流上的非洛伦兹力？
作者：
A. Hillas
Graneau1已经报道了两个例子，电磁力作用在电流元素上，显然作用在电流的方向上，而不是普遍接受的洛伦兹力，后者总是与电流成直角作用，他认为这些观察结果支持安培关于两个电流元素之间作用力的旧公式。然而，首先，这两个观察结果都可以用洛伦兹力来理解，因为在所给的例子中，电流流线从收缩点发散，因此局部产生的磁场施加垂直于电流的力，产生平行于发散电流的对称轴的力的分量，方向远离顶点。在“铜潜艇”的情况下，定量检查是可能的，长铜棒(半径a==1.5 mm)，一端钝化，但另一端逐渐变细，当放置在水银槽(0.25平方英尺)中时，它会淹没自己。英寸横截面)，携带400A电流(/)，并沿着槽以15埃S-1的速度前进，尖端总是拖尾。由于铜的高导电性，许多电流将被输送到距离该点不远的铜中，在向铜的较宽部分移动时，电流线将从那里分散开来，在这个锥形部分中，洛伦兹力有一个平行于轴的分量，磁力线绕着轴旋转。(离开钝端后，电流将再次发散，对水银施加推动力。)取汞的单位长度的电阻是铜的全宽时的k(=2.67)倍，并假设在垂直于中心轴的任何平面上，每个介质中的电流密度几乎均匀且与电导率成比例，洛伦兹力可以在铜的整个锥形截面上积分，从而得到总的纵向力f。Lol2F/4TT(SI单位)，其中F=hln(1+k)-(k/1+k)-！(K/1+k)2}，指向远离顶点。运动基本上被惯性力=pv21ra2(忽略流体的任何运动)所阻挡，p是水银的密度。这给出了速度v=0.16m，S--与观测结果很好地吻合。在引用的另一个观察中，当汞从固定导线的末端流出时，电流会分散到汞中，因此在分叉点附近施加一个力，指向远离导线的方向。其次，人们不能通过实验来区分作用在两个物体上的相互作用力的两个不同的定律。
Two instances have been reported by Graneau1 of an electromagnetic force on a current element apparently acting in the direction of current flow, in contrast to the generally accepted Lorentz force which always acts at right angles to the current, and he believes that these observations support instead Ampere's older formula for the force acting between two current elements. In the first place, however, both observations can be understood in terms of Lorentz forces, for in the examples given, the current flow lines diverge from a point of constriction, so that the locally generated magnetic field exerting a force normal to the current produces a component of force parallel to the axis of symmetry of the diverging current, directed away from the apex. A quantitative check is possible in the case of the'copper submarine', the long copper rod (radius a== 1.5 mm), blunt at one end but tapered to a point at the other, which submerged itself when placed in a trough of mercury (0.25 sq. inch cross-section) carrying a 400 A current (/), and travelled along the trough at a speed of 15 em s-1, always with the pointed end trailing. Because of the high conductivity of copper, much of the current will be funnelled into the copper not far from the point, from where the lines of current flow will spread apart somewhat on moving towards the wider part of the copper, and in this cone section the Lorentz force has a component parallel to the axis, the magnetic field lines being circles around the axis.(After leaving the blunt end, the current will again diverge, exerting a propulsive force on the mercury.) Taking the resistance per unit length of the mercury to be k (= 2.67) times that of the copper at its full width, and assuming that in any plane normal to the central axis the current density is nearly uniform in each medium and in proportion to conductivity, the Lorentz forces can be integrated over the whole of the cone section of the copper, to give the total longitudinal force f. Lol2F/4TT (SI units), where F== Hln (1+ k)-(k/1+ k)-!(k/1+ k) 2}, directed away from the apex. The motion is resisted essentially by the inertial force= pv21ra2 (neglecting any motion of the fluid), p being the density of mercury. This gives a velocity v= 0.16 m s-\in good agreement with observation. In the other observation cited, where mercury flowed away from the end of a stationary wire carrying a current, the current would fan out into the mercury and so exert a force near the point of divergence, directed away from the wire. Second, one cannot distinguish by experiment between the two different laws for the mutual forces acting on two