Dimensional formula of Displacement current

How to get the dimensional formula of displacement current

1. Start from the definition: displacement current = permittivity of free space × electric flux / time.
2. electric charge = electric current × time, so electric charge is [A] × [T] = [T A].
3. velocity = length / time, so velocity is [L] / [T] = [L T^-1].
4. acceleration = velocity / time, so acceleration is [L T^-1] / [T] = [L T^-2].
5. force = mass × acceleration, so force is [M] × [L T^-2] = [M L T^-2].
6. permittivity of free space = electric charge² / (force × length²), so permittivity of free space is [T A]² / ([M L T^-2] × [L]²) = [M^-1 L^-3 T⁴ A²].
7. electric field = force / electric charge, so electric field is [M L T^-2] / [T A] = [M L T^-3 A^-1].
8. Put in the dimension of each part: [M^-1 L^-3 T⁴ A²] × [M L³ T^-3 A^-1] / [T].
9. Add the powers of each base quantity: [A].

Quantities with the dimensions [A]

• Electric current

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

Three questions on displacement current

Related quantities

• L Self inductance [M L² T⁻² A⁻²]
• M Mutual inductance [M L² T⁻² A⁻²]
• 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]