Transverse and longitudinal noise

Abstract

Analytic functions are derived for the spectral noise voltage density between two circular sensor electrodes on a two‐dimensional isotropic conductor, placed either transversely or longitudinally to a homogeneous electric field. The sensor electrodes are far removed from both the bias electrodes and the boundaries. The relations have been checked experimentally for 1/f conductivity fluctuations. Both the transverse and longitudinal noise are proportional to I⁻²F_s(J⋅J̃)² ds where J⋅J̃ represents the dot (scalar) product of the homogeneous current density J and the adjoint current density J̃, and the current through the bias electrodes is I. It is found that the transverse noise is somewhat smaller than the longitudinal noise.