Two Et–Wash torsion balance instruments exploited optimized Fourier–Bessel geometries to test the short-distance properties of gravity and to constrain exotic dipole–dipole and monopole–dipole interactions. We discuss efficient analytic techniques for computing the expected torques in those instruments arising from Newtonian and Yukawa interactions between unpolarized test bodies and dipole–dipole and monopole–dipole torques on polarized test-bodies. We consider systematic effects induced by weak external magnetic fields on the nominally unpolarized test-bodies. We also present a new Fourier–Bessel expansion for inverse-power-law (IPL) potentials and use this to calculate the expected IPL signals in our recent short-distance test of the gravitational inverse-square law. Our results slightly improve limits on inverse-5th-power law potentials.

两个 Et-Wash 扭力天平仪器利用优化的傅立叶-贝塞尔几何结构来测试重力的短距离特性并限制奇异的偶极-偶极和单极-偶极相互作用。我们讨论了有效的分析技术，用于计算那些仪器中未极化测试体之间的牛顿和汤川相互作用以及极化测试体上的偶极 - 偶极和单极 - 偶极扭矩产生的预期扭矩。我们考虑由弱外部磁场对名义上未极化的测试体引起的系统影响。我们还提出了反幂律 (IPL) 势的新傅立叶-贝塞尔展开式，并在我们最近的引力平方反比定律短距离测试中使用它来计算预期的 IPL 信号。我们的结果略微改善了对反五次幂律势的限制。