A coil of wire 0.25 m long and having 400 turns carries a...

A coil of wire $0.25 \mathrm{m}$ long and having 400 turns carries a current of $15 \mathrm{A}$. (a) What is the magnitude of the magnetic field strength $H ?$ (b) Compute the flux density $B$ if the coil is in a vacuum. (c) Compute the flux density inside a bar of chromium that is positioned within the coil. The susceptibility for chromium is found in Table 20.2. (d) Compute the magnitude of the magnetization $M$.

A coil of wire $0.25 \mathrm{m}$ long and having 400 turns carries a current of $15 \mathrm{A}$.
(a) What is the magnitude of the magnetic field strength $H ?$
(b) Compute the flux density $B$ if the coil is in a vacuum.
(c) Compute the flux density inside a bar of chromium that is positioned within the coil. The susceptibility for chromium is found in Table 20.2.
(d) Compute the magnitude of the magnetization $M$.

Key Concepts

Magnetic Field Strength (H)

This concept refers to the measure of the magnetomotive force per unit length of a magnetic circuit. In the context of a solenoid or coil, H is calculated by dividing the product of the number of turns and the current by the length of the coil. It represents the strength of the magnetic field produced by the current-carrying coil independent of the medium in which it is placed.

Magnetic Flux Density in Vacuum (B)

Magnetic flux density, B, indicates the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. In a vacuum (or free space), B is directly proportional to the magnetic field strength H, with the proportionality constant being the permeability of free space (??). This relationship is expressed as B = ??H.

Magnetic Susceptibility and Relative Permeability

Magnetic susceptibility (?) is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. It relates to the relative permeability (?r) of a material through the relation ?r = 1 + ?. When a material like a magnetic bar is introduced into a coil, its intrinsic magnetic properties modify the total magnetic flux density, B, by scaling the field strength H with the material's relative permeability.

Magnetization (M)

Magnetization is the measure of the magnetic moment per unit volume within a material, expressing how much a material becomes magnetized when exposed to a magnetic field. It is directly proportional to the magnetic field strength H through the material's magnetic susceptibility, given by M = ?H. This concept is vital for determining the overall magnetic response of a material when subjected to an external magnetic field.

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