What happens to the self-inductance of a long air-cored solenoid if its core is replaced by a soft iron cylinder?

💡 Solution & Explanation

The self-inductance of a long air-cored solenoid is directly proportional to the absolute magnetic permeability of its core medium. Replacing air with a soft iron cylinder dramatically elevates the permeability of the core, leading to a massive surge in magnetic flux linkage per unit current. Consequently, the self-inductance increases significantly. Soft iron is a ferromagnetic material characterized by high magnetic permeability and low retentivity, making it ideal for electromagnets and transformer cores.