Dimensional formula of Magnetic susceptibility

How to get the dimensional formula of magnetic susceptibility

1. Start from the definition: magnetic susceptibility = magnetisation / magnetic field strength.
2. area = length × length, so area is [L] × [L] = [L²].
3. magnetic moment = electric current × area, so magnetic moment is [A] × [L²] = [L² A].
4. volume = length³, so volume is [L]³ = [L³].
5. magnetisation = magnetic moment / volume, so magnetisation is [L² A] / [L³] = [L^-1 A].
6. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
7. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
8. Put in the dimension of each part: [L^-1 A] / [L^-1 A].
9. 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
• Relative permeability
• Power factor
• Quality factor
• Refractive index
• Magnification

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

Three questions on magnetic susceptibility

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]