A relation between physical consequences of the so-called Ehrenfest's Paradox and the radial electric field E r (r) in the classical quasi-neutral tokamak plasma is shown. Basic author's approach to the relativistic nature of the tokamak E r (r) has been described in Romannikov (J. Exp. Theor. Phys. 108:340-348, 2009). The experiment which can resolve the Ehrenfest's Paradox is presented.