Dimensional formula of Relative permeability

How to get the dimensional formula of relative permeability

1. Start from the definition: relative permeability = magnetic field / magnetic field.
2. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
3. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
4. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
5. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
6. magnetic field = force / (electric charge × velocity), so magnetic field is [M L T^-2] / ([T A] × [L T^-1]) = [M T^-2 A^-1].
7. Put in the dimension of each part: [M T^-2 A^-1] / [M T^-2 A^-1].
8. Add the powers of each base quantity: [M⁰ L⁰ T⁰].

Quantities with the dimensions [M⁰ L⁰ T⁰]

• Angle
• Solid angle
• Coefficient of friction
• Coefficient of restitution
• Relative density
• Strain
• Poisson's ratio
• Reynolds number
• Emissivity
• Ratio of specific heats
• Sound level
• Relative permittivity
• Magnetic susceptibility
• Power factor
• Quality factor
• Refractive index
• Magnification

Equal dimensions do not make them the same quantity. Compare relative permeability with the others in the full grid.

Three questions on relative permeability

Related quantities

• B Magnetic field [M T⁻² A⁻¹]
• Φ_B Magnetic flux [M L² T⁻² A⁻¹]
• m Magnetic moment [L² A]
• H Magnetising field [L⁻¹ A]
• M Magnetisation [L⁻¹ A]
• m_p Magnetic pole strength [L A]