# Dimensions of Permeability

## Dimensional Formula of Permeability

The dimensional formula of permeability is given by,

[MLT-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 LT-2] . . . (3)

Current = [M0 LT0 I1] . . . (4)

Length = [M0 LT0] . . . . . (5)

On substituting equation (3), (4) and (5) in equation (2) we get,

Magnetic flux density = Force × [Current × Length]-1

= [M1 LT-2] × [M0 LT0 I× M0 LT0]-1

Therefore, the dimensional formula of magnetic flux density = [M1 LT-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 LT-2 I-1] × [M0 L-1 T0 I1]-1 = [MLT-2 I-2]

Therefore, the magnetic permeability is dimensionally represented as [MLT-2 I-2].