Determine the dimensional equations for power, energy density, voltage, and permittivity.

Power ($P$) is the rate at which work ($W$) is done.

Work ($W$) = Force ($F$) $\times$ Distance ($L$)
Force ($F$) = Mass ($M$) $\times$ Acceleration ($a$)
Acceleration ($a$) = $\frac{\text{Distance}}{\text{Time}^2} = L T^{-2}$

The dimensional equation of power is $\boxed{M L^2 T^{-3}}$.

b) (ii)

Energy density ($W_d$) is energy per unit volume.
Energy ($E$) has dimensions $M L^2 T^{-2}$.
Volume ($Vol$) has dimensions $L^3$.

Distance ($d$) has dimensions $L$.

Voltage ($V$) is work per unit charge. Charge ($Q$) = Current ($I$) $\times$ Time ($T$).

Permittivity ($\epsilon$) can be derived from Coulomb's law $F