Changing the core material of a solenoid affects the induced current primarily during the transition phases when the current is applied or removed. In a DC solenoid, the current change is influenced by the solenoid arm's position, which alters the inductance and slows the current rise. The magnetic permeability of the core material plays a crucial role in this process, especially if the core is ferromagnetic. Additionally, the mechanical load against which the arm moves further impacts the current change. Understanding these factors is essential for analyzing the behavior of solenoid loops under varying core materials.