圆柱几何中的静电贴片效应。III。扭矩
Electrostatic Patch Effect in Cylindrical Geometry. III. Torques
摘要：
本文从文献[1]和[2]出发，继续研究了两个平行轴的圆柱形导体在不均匀电压分布下的静电力矩。我们计算的静电势和能量的最低阶的间隙圆柱半径比为任意相对旋转的圆柱体的对称轴。通过能量守恒，轴向转矩，独立于均匀电压差，被发现作为在旋转角的能量的导数。我们还推导出轴向和倾斜扭矩的表面积分法：扭矩矢量是表面元素上的静电力和它的位置矢量的叉积的圆柱表面上的积分。倾斜力矩由两部分组成：一部分来自贴片与均匀电压之间的相互作用，另一部分来自贴片之间的相互作用。扭矩的一般属性进行了描述。文[2]中提出的一个方便的局部化模型被用来计算力矩的初等函数。在此基础上，我们详细分析了一对贴片的相互作用，即扭矩对贴片参数（宽度和强度）和它们的相互位置的依赖关系。轴向扭矩的影响，然后研究的STEP任务的实验条件。
英文摘要：
We continue to study the effect of uneven voltage distribution on two close cylindrical conductors with parallel axes started in our papers [1] and [2], now to find the electrostatic torques. We calculate the electrostatic potential and energy to lowest order in the gap to cylinder radius ratio for an arbitrary relative rotation of the cylinders about their symmetry axis. By energy conservation, the axial torque, independent of the uniform voltage difference, is found as a derivative of the energy in the rotation angle. We also derive both the axial and slanting torques by the surface integration method: the torque vector is the integral over the cylinder surface of the cross product of the electrostatic force on a surface element and its position vector. The slanting torque consists of two parts: one coming from the interaction between the patch and the uniform voltages, and the other due to the patch interaction. General properties of the torques are described. A convenient model of a localized patch suggested in [2] is used to calculate the torques explicitly in terms of elementary functions. Based on this, we analyze in detail patch interaction for one pair of patches, namely, the torque dependence on the patch parameters (width and strength) and their mutual positions. The effect of the axial torque is then studied for the experimental conditions of the STEP mission.
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