since is the heat produced by the conduction current , this expression is easily to be calculated numerically (however, an unobservable value will be obtained).
If one now asks oneself, as to how this result (which contradicts the relativity principle) can arise, then one sees that one hasn't actually calculated the force acting upon the matter of the conductor, but the force which acts upon the electrons moving in the interior of the conductor. The latter forces are still to be transfered to matter by individually unknown forces, and this only happens (without change of the magnitude) when equality between action and reaction exists for the forces between matter and electrons. However, for moving bodies, the action is not equal to the reaction according to the relativity principle, and this circumstance exactly cancels the force of Liénard.
In summary one can say, that there is little prospect of testing the relativity principle by experiment; except some astronomic observations, only the measurement of the mass of electrons comes into account. Though one shall not forget, that the negative outcome of different experiments such as Michelson's interference experiment and the experiments to demonstrate double refraction due to Earth's motion, could only be explained by the relativity principle.