Ask HN: A dumb game of dimensional analysis

I thought a few weeks ago, that there might be a dimensional ladder for EM, but I can't figure out how turn into something usable. I'm sharing some of my markdown notes, now frustrated.

Starting from how an Ampere used to be defined (N/m, kg/s2)...

- V = Voltage, in Volts, (pre-2019 equal to m2/s)

- Q = Charge, in Coulombs, (pre-2019 equal to kg/s)

*Inertial Surfaces (J·s²)*

  ∫V dt × ∫Q dt = m² × kg

*Modes of Action (J·s)*

  V × ∫Q dt = (m²/s) × kg

  ∫V dt × Q = m² × (kg/s)

*Energy, Patterns of Stress (J)*

  dV/dt × ∫Q dt = (m²/s²) × kg

  V × Q = (m²/s) × (kg/s)

  ∫V dt × dQ/dt = m² × (kg/s²)

*Power, Waves of Stress (J/s)*

  dV/dt × Q = (m²/s²) × (kg/s)

  V × dQ/dt = (m²/s) × (kg/s²)

*Impulse, Wave Conversions (J/s²)*

  dV/dt × dQ/dt = (m²/s²) × (kg/s²)

*Spatial Derivatives, Effects on... 'Matter'?*

- d(Surface)/dx ~ Transport

- d(Action)/dx ~ Momentum

- d(Energy)/dx ~ Force

- d(Power)/dx ~ ??? Propagation?

- d(Impulse)/dx ~ ??? Conversion?

*Spatial Integrals, Effects on... 'Space'?*

- ∫(Surface)dx ~ Inertial Volume

- ∫(Action)dx ~ kgm3/s

- ∫(Energy)dx ~ kgm3/s2

- ∫(Power)dx ~ kgm3/s3

- ∫(Impulse)dx ~ kgm3/s4

In the wave modes for Power, 'Phase' = dV/dt, Charge = Q, with Heaviside's wave equation `d2(Volts)/dt2 + v2 * d2(Current)/dx2 = d2(Current)/dt2 + v2 * d2(Volts)/dx2` would then.... `d2(Phase)/dt2 + u2 * d2(Charge)/dx2 = d2(Charge)/dt2 + u2 * d2(Phase)/dx2` where v2 = 1 / LC, u2 = 1 / ??