Magnetic Johnson-Nyquist noise (JNN) originating from metal electrodes, used to create a static electric field in neutron electric-dipole-moment (nEDM) experiments, may limit the sensitivity of measurements. We present here the first dedicated study on JNN applied to a large-scale long-measurement-time experiment with the implementation of a co-magnetometry. In this study, we derive surface- and volume-averaged root-mean-square normal noise amplitudes at a certain frequency bandwidth for a cylindrical geometry. In addition, we model the source of noise as a finite number of current dipoles and demonstrate a method to simulate temporal and three-dimensional spatial dependencies of JNN. The calculations are applied to estimate the impact of JNN on measurements with the new apparatus, n2EDM, at the Paul Scherrer Institute. We demonstrate that the performances of the optically pumped $^{133}$Cs magnetometers and $^{199}$Hg co-magnetometers, which will be used in the apparatus, are not limited by JNN. Further, we find that in measurements deploying a co-magnetometer system, the impact of JNN is negligible for nEDM searches down to a sensitivity of $4,times,10^{-28},ecdot{rm cm}$ in a single measurement; therefore, the use of economically and mechanically favored solid aluminum electrodes is possible.
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