Dimensional formula of Magnetising field

How to get the dimensional formula of magnetising field

1. Start from the definition: magnetising field = magnetic field / permeability of free space.
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. permeability of free space = force / electric current², so permeability of free space is [M L T^-2] / [A]² = [M L T^-2 A^-2].
8. Put in the dimension of each part: [M T^-2 A^-1] / [M L T^-2 A^-2].
9. Add the powers of each base quantity: [L^-1 A].

Quantities with the dimensions [L⁻¹ A]

• Magnetisation

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

Three questions on magnetising field

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]
• χ Magnetic susceptibility [M⁰ L⁰ T⁰]
• μ_r Relative permeability [M⁰ L⁰ T⁰]
• m_p Magnetic pole strength [L A]