How does magnetic permeability affect an electromagnet’s strength?

Magnetic permeability ($\mu$) is a fundamental property that significantly enhances the strength of an electromagnet. It represents a material's ability to support the formation of a magnetic field within itself.1

In an electromagnet, a core made of a material with high magnetic permeability—such as iron—is placed inside a coil of wire. When an electric current flows through the coil, it creates a magnetizing field ($H$). The core material concentrates the magnetic flux lines, resulting in a much higher magnetic flux density ($B$) than would exist in a vacuum or air.12

The relationship is defined by the equation $B=\mu H$. Because the reluctance of a magnetic circuit is inversely proportional to permeability ($r=l/\mu A$), a higher $\mu$ reduces the circuit's reluctance, allowing for a greater magnetic flux for a given amount of current. Essentially, by using a core with high permeability, an electromagnet can produce a significantly stronger magnetic field in a specific region, such as a narrow gap, compared to a coil without such a core.32