https://www.researchgate.net/publication/281303991_The_Repulsive_Force_Within_Ampere's_Bridge_Explained_by_Coulomb's_Law_and_Special_Relativity_Theory_Taking_into_Account_the_Effects_of_Propagation_Delay
It has been previously proved that the repulsive force between the two parts of Ampère’s bridge, measured in experiments performed by Pappas and Moyssides, can be explained by Coulomb’s law, if the effects of propagation delay are correctly taken into account. Special relativity theory is also necessary to estimate the extent to which it may affect the result. Otherwise it might be unnecessary to involve special relativity theory in the case of DC currents carried by electric conductors, because the velocities of conduction electrons are usually very small compared to the speed of light. However, in this paper, the force between the two parts of Ampère’s Bridge has been calculated, taking into account special relativity theory, particularly the Lorentz transformation which brings about a change in the lengths of moving bodies. The result is that the repulsive force between the two parts of Ampère’s bridge remains repulsive, displaying dependence on the thickness of the branches, decreasing with increasing thickness. This was also the case when analysis was conducted without taking into account the special relativity theory. In fact, the predictions are in complete agreement with physical measurements.
