If the same amperage is passed through a 25 mm diameter bar and a 51 mm diameter bar of the same length and material, what will be the strength of the magnetic field at the center of both bars?

The correct rationale for the scenario involves understanding the properties of magnetic fields generated by current-carrying conductors. When a cylindrical conductor, such as a bar, has an alternating or direct current passed through it, the magnetic field strength is influenced by its diameter.

In the case of concentric cylindrical conductors, the magnetic field inside a solid conductor is indeed zero at the center of the conductor when the current is uniformly distributed. This is due to the way magnetic fields behave in a conductor: the contributions to the magnetic field from the currents in the outer layers exactly cancel out the contributions from currents in the inner layers at the center.

As such, regardless of whether the bar's diameter is 25 mm or 51 mm, the magnetic field strength at the geometric center of both bars will remain zero when the same current is applied throughout their length. Hence, selecting that the magnetic field strength at the center of both bars is zero accurately reflects the fundamental principle of magnetostatics in conductors.