Explain, in terms of magnetic permeability, why inserting a soft-iron core inside a current-carrying solenoid

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Q. Explain, in terms of magnetic permeability, why inserting a soft-iron core inside a current-carrying solenoid greatly increases the magnetic field it produces, compared to an identical air-core solenoid carrying the same current.

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For a solenoid of $n$ turns per unit length carrying current $I$ , the field is $B=\mu_r\mu_0nI$ (Section 1.15), where $\mu_r$ is the relative permeability of whatever fills the solenoid's interior. For an air core, $\mu_r\approx1$ , so $B\approx\mu_0nI$ . For a soft-iron core, $\mu_r$ is typically in the hundreds to low thousands (Section 1.14), so, for the IDENTICAL winding and current, the field is multiplied by that same large factor. …

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Q.Explain, in terms of magnetic permeability, why inserting a soft-iron core inside a current-carrying solenoid greatly increases the magnetic field it produces, compared to an identical air-core solenoid carrying the same current.

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Q.Explain, in terms of magnetic permeability, why inserting a soft-iron core inside a current-carrying solenoid greatly increases the magnetic field it produces, compared to an identical air-core solenoid carrying the same current.

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