Dimensional formula of Self inductance

How to get the dimensional formula of self inductance

1. Start from the definition: self inductance = magnetic flux / electric current.
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. area = length × length, so area is [L] × [L] = [L²].
8. Put in the dimension of each part: [M L² T^-2 A^-1] / [A].
9. Add the powers of each base quantity: [M L² T^-2 A^-2].

Quantities with the dimensions [M L² T⁻² A⁻²]

• Mutual inductance

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

Three questions on self inductance

Related quantities

• X Reactance [M L² T⁻³ A⁻²]
• X_L Inductive reactance [M L² T⁻³ A⁻²]
• X_C Capacitive reactance [M L² T⁻³ A⁻²]
• Z Impedance [M L² T⁻³ A⁻²]
• cos φ Power factor [M⁰ L⁰ T⁰]
• Q Quality factor [M⁰ L⁰ T⁰]