Magnetic Circuit and Electromagnetism - Relation between the Magnetic Field Intensity (H) and the Magnetic Flux Density (B)
1 Answer
In electromagnetism, the relationship between the magnetic field intensity (H) and the magnetic flux density (B) is governed by the material properties of the medium through which the magnetic field passes. This relationship is described by Ampere's law and the concept of magnetic permeability.
Ampere's Law:
Ampere's law states that the circulation of the magnetic field intensity around a closed path (loop) is proportional to the total current passing through the enclosed area. Mathematically, Ampere's law is expressed as:
∮H * dl = I_enclosed,
where:
∮H * dl represents the integral of the magnetic field intensity (H) around a closed path (loop).
I_enclosed is the total current passing through the area enclosed by the loop.
Magnetic Permeability (μ):
Magnetic permeability is a material property that relates the magnetic field intensity (H) to the magnetic flux density (B). It quantifies how easily a material can be magnetized by an applied magnetic field. The relationship between H and B is given by:
B = μ * H,
where:
B is the magnetic flux density (measured in Tesla, T).
μ (mu) is the magnetic permeability of the material (measured in Henrys per meter, H/m).
H is the magnetic field intensity (measured in Ampere per meter, A/m).
For linear, isotropic materials (materials that respond linearly to the magnetic field), the relationship between H and B is straightforward and proportional, and the value of μ is constant. However, for nonlinear or anisotropic materials, this relationship might be more complex and could vary with the strength of the applied field.
Permeability of Free Space (μ₀):
In vacuum or free space, the magnetic permeability is denoted as μ₀ (mu naught) and has a constant value:
μ₀ = 4π * 10^-7 H/m.
This value defines the permeability of free space and serves as a reference point for comparing the permeability of other materials.
In summary, the relationship between the magnetic field intensity (H) and the magnetic flux density (B) is described by the magnetic permeability (μ) of the material through which the magnetic field passes. For most practical purposes, this relationship is linear and is given by B = μ * H, where μ can vary based on the material being considered.
Ampere's Law:
Ampere's law states that the circulation of the magnetic field intensity around a closed path (loop) is proportional to the total current passing through the enclosed area. Mathematically, Ampere's law is expressed as:
∮H * dl = I_enclosed,
where:
∮H * dl represents the integral of the magnetic field intensity (H) around a closed path (loop).
I_enclosed is the total current passing through the area enclosed by the loop.
Magnetic Permeability (μ):
Magnetic permeability is a material property that relates the magnetic field intensity (H) to the magnetic flux density (B). It quantifies how easily a material can be magnetized by an applied magnetic field. The relationship between H and B is given by:
B = μ * H,
where:
B is the magnetic flux density (measured in Tesla, T).
μ (mu) is the magnetic permeability of the material (measured in Henrys per meter, H/m).
H is the magnetic field intensity (measured in Ampere per meter, A/m).
For linear, isotropic materials (materials that respond linearly to the magnetic field), the relationship between H and B is straightforward and proportional, and the value of μ is constant. However, for nonlinear or anisotropic materials, this relationship might be more complex and could vary with the strength of the applied field.
Permeability of Free Space (μ₀):
In vacuum or free space, the magnetic permeability is denoted as μ₀ (mu naught) and has a constant value:
μ₀ = 4π * 10^-7 H/m.
This value defines the permeability of free space and serves as a reference point for comparing the permeability of other materials.
In summary, the relationship between the magnetic field intensity (H) and the magnetic flux density (B) is described by the magnetic permeability (μ) of the material through which the magnetic field passes. For most practical purposes, this relationship is linear and is given by B = μ * H, where μ can vary based on the material being considered.