Experimental Test of Coulomb's Law

One of the classic "null experiments" tests the exactness of the electrostatic inverse-square law. The outer shell of a spherical capacitor is raised to a potential $V$ with respect to a distant ground, and the potential difference $\Delta V$ induced between the inner and outer shells is measured. If this induced potential difference is not zero, Coulomb's law is violated. For example, if we assume that the force between charges varies as $r^{-2+q}$, then $\frac{\Delta }{V}$ is approximately a tenth of $q$. In our experiment five concentric spheres are used. A potential difference of 40 kV at 2500 Hz is impressed between the outer two spheres. A lock-in detector with a sensitivity of about 0.2 nV measures the potential difference between the inner two spheres. We find $\mathrm{}\left|q\right|\mathrm{}\le 1.3\times {10}^{-13\mathrm{}}$. We also find comparable limits on the detected signal when the operating frequency is 250 Hz, and when the detector is synchronized with the charging current rather than with the charge itself.