1Which is the dimensional formula of permeability of free space?
Permeability of free space works out to [M L T⁻² A⁻²].
Fundamental constantsClass 12, Moving Charges and Magnetism
Dimensional formula of Permeability of free space
[M L T-2 A-2]
The μ0 in the force between currents, F/L = μ0 I1 I2/(2πd). Together with ε0 it fixes the speed of light.
How to get the dimensional formula of permeability of free space
- Start from the definition: permeability of free space = force / electric current2.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- Put in the dimension of each part: [M L T-2] / [A]2.
- Add the powers of each base quantity: [M L T-2 A-2].
Three questions on permeability of free space
2What is the SI unit of permeability of free space?
The SI unit of permeability of free space is the henry per metre (H/m).
3Do permeability of free space and Planck's constant have the same dimensions?
Permeability of free space is [M L T⁻² A⁻²] but Planck's constant is [M L² T⁻¹].
An equation that uses permeability of free space
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
c = 1 / sqrt(μ0 ε0)c[L T-1]=1/sqrt(mu0 epsilon0)[L T-1]Dimensionally consistentEvery term is [L T-1]
μ0 = permeability of free spaceε0 = permittivity of free space
Permeability of free space: quick answers
What is the dimensional formula of permeability of free space?
The dimensional formula of permeability of free space is [M L T⁻² A⁻²]. It comes from permeability of free space = force / electric current².
What is the SI unit of permeability of free space?
The SI unit of permeability of free space is the henry per metre (H/m).
Is permeability of free space dimensionless?
No. Permeability of free space has the dimensions [M L T⁻² A⁻²].