Dimensional Formula of Permeability

The dimensional formula of permeability is given by,

[M¹ L¹ T^-2 I^-2]

Where,

• M = Mass
• I = Current
• L = Length
• T = Time

Derivation

Magnetic Permeability (μ) = Magnetic flux density × [Magnetic field strength]^-1 . . . . (1)

Since, Force = magnetic flux density × current × length

Therefore, magnetic flux density = Force × [Current × Length]^-1 . . . . (2)

⇒ The dimentional 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].

⇒ Check Other Dimensional Formulas:

• Dimensions of Coefficient of Friction
• Dimensions of Charge
• Dimensions of Reynolds Number
• Dimensions of Magnetic Flux
• Dimensions of Gravitational Potential Energy