A 50-cm -long solenoid has 100 turns of wire and carries a...

A $50-\mathrm{cm}$ -long solenoid has 100 turns of wire and carries a current of $0.95 \mathrm{~A}$. It has a ferromagnetic core completely filling its interior where the field is $0.71 \mathrm{~T}$. Determine the (a) magnetic permeability and (b) relative magnetic permeability of the material.

Key Concepts

Magnetic Permeability

Magnetic permeability is a fundamental property of a material that quantifies its ability to support and enhance the formation of a magnetic field. It is a measure of how easily a magnetic field can induce magnetization within the material. Higher permeability means that the material can concentrate magnetic flux more efficiently.

Relative Magnetic Permeability

Relative magnetic permeability is a dimensionless ratio that compares the permeability of a material to the permeability of free space (vacuum). It indicates how many times better (or worse) the material is at conducting magnetic flux compared to a vacuum, serving as a key parameter in understanding magnetic behavior in various materials.

Magnetic Field in a Solenoid

The magnetic field within a solenoid is generated when an electric current flows through many closely spaced turns of wire. The field inside a solenoid is approximately uniform and is directly proportional to both the current and the density of turns (number of turns per unit length). This concept is central in demonstrating how electric currents can create concentrated and controlled magnetic fields.

Ampere's Law

Ampere's Law is a fundamental principle that relates the integrated magnetic field around a closed loop to the total electric current passing through the loop. It is instrumental in deriving expressions for the magnetic field in systems with high symmetry, such as solenoids, and underpins the theoretical framework used to calculate magnetic fields and permeability.

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