Changing the diameter of a wire does not affect the magnetic field at a fixed point if the current remains constant, as the magnetic field is primarily dependent on the current and the distance from the wire. The discussion highlights confusion regarding measurements taken at very small scales, suggesting that measurement errors could be influencing the observed changes in the magnetic field. The placement of the wire is crucial, as a thicker wire may have parts that are farther from the measurement point, potentially skewing results. The participants emphasize the importance of accurate measurement techniques in such small-scale experiments. Overall, the relationship between wire diameter and magnetic field strength under fixed current conditions is clarified.