Permeability refers to the ability of a material to allow the passage of magnetic lines of force through it. It measures how well a material supports the formation of a magnetic field within itself.
The dimensional formula of permeability is [M1 L1 T-2 I-2]
Where,
Magnetic Permeability (μ) = Magnetic flux density × [Magnetic field strength]-1 . . . . (1)
Therefore, magnetic flux density = Force × [Current × Length]-1 . . . . (2)
The dimensional formula of,
Force = [M1 L1 T-2] . . . (3)
Current = [M0 L0 T0 I1] . . . (4)
Length = [M0 L1 T0] . . . . . (5)
On substituting equation (3), (4) and (5) in equation (2) we get,
Magnetic flux density = Force × [Current × Length]-1
[M1 L1 T-2] × [M0 L0 T0 I]-1 × M0 L1 T0]-1
Therefore, the dimensional formula of magnetic flux density = [M1 L0 T-2 I-1] . . . . (6)
And, the dimensions of Magnetic field strength = [M0 L-1 T0 I1] . . . . . (7)
On substituting equation (6) and (7) in equation (1) we get,
Magnetic Permeability = Magnetic flux density × [Magnetic field strength]-1
Or, μ = [M1 L0 T-2 I-1] × [M0 L-1 T0 I1]-1 = [M1 L1 T-2 I-2]
Therefore, the magnetic permeability is dimensionally represented as [M1 L1 T-2 I-2].
Also Check: Dimension of Acceleration
Permeability dimensional analysis helps us verify equations and understand its physical significance. For instance, the permeability of free space (μ0) is:
4π × 10-7 H/m
The magnetic permeability units are expressed in henry per meter (H/m). This SI unit is fundamental in electromagnetism and material science.
In the SI system, permeability is measured in henry per meter (H/m), derived from the equations of electromagnetism.
Permeability measurement units vary. In the CGS system, it is measured in Gauss per Oersted, but H/m is more commonly used.
The magnetic permeability formula is:
μ = μr μ0
Where:
The permeability coefficient units describe magnetic properties of materials and are used in fields like transformer design and electromagnetic shielding.
The magnetic permeability dimensional formula ([M1 L1 T-2 I-2]) ensures compatibility in electromagnetic equations.
The permeability of free space units (μ0) is a universal constant:
4π × 10-7 H/m
This constant plays a fundamental role in defining the speed of electromagnetic waves in a vacuum.
Understanding permeability is critical for:
Permeability () is a measure of a material's ability to support the formation of a magnetic field within itself. It describes how a material responds to a magnetic field and how easily magnetic field lines can pass through it.
The dimensional formula of permeability (μ) is [M1 L1 T-2 I-2]. This formula shows the dependency of permeability on mass (M), length (L), time (T), and electric current (I).
The formula for permeability (μ) is μ = μr × μ0
Where:
The SI unit of permeability is henry per meter (H/m), which can also be expressed as newton per ampere squared (N·A-2).