Stuck on this dimensional analysis question.

1. The problem statement, all variables and given/known data

The total power radiated by an oscillating electric dipole is a function of the oscillation frequency ω, the dipole moment p(=Qd, where ±Q is the charge at each end of the dipole and d is the distance between charges), the speed of light c and the permittivity of free space ε₀. Apply dimensional analysis to find the form of this function. Hence find the ratio of the power emitted by the same dipole at frequencies ω and 2ω



2. Relevant equations







3. The attempt at a solution

I started off by writing out the units and trying to find the powers, this left me with:

J/s ∝ (Hz)^A (Qm)^B (m/s)^C (F/m)^D

My first thought was that C=1, so that there is s^-1 on each side.

Then I thought that D=2 so that the metres cancel out.

Then I'm left with J ∝ (Hz)^A Q F² /s

And now I'm completely stuck :(

Any help appreciated, thanks.

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

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