Dimensional formula of Poynting vector

How to get the dimensional formula of Poynting vector

1. Start from the definition: Poynting vector = electric 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. electric field = force / electric charge, so electric field is [M L T^-2] / [T A] = [M L T^-3 A^-1].
7. magnetic field = force / (electric charge × velocity), so magnetic field is [M L T^-2] / ([T A] × [L T^-1]) = [M T^-2 A^-1].
8. Put in the dimension of each part: [M L T^-3 A^-1] × [M T^-2 A^-1] / [M L T^-2 A^-2].
9. Add the powers of each base quantity: [M T^-3].

Quantities with the dimensions [M T⁻³]

• Heat flux
• Solar constant
• Intensity of a wave

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

Three questions on Poynting vector

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]