In my textbook, there is a following task (that's my translation and it may not be 100% clear or accurate, so feel free to request additional clarification)

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> A flat capacitor, charged with charge $Q$, with conductive plates of equal areas $S$, height $h$ and distance between them $d$ was positioned vertically, that is, in the way that the bottom edges of conductive fields touch a dielectric fluid (i.e. water, of density $\rho$ and relative permittivity $\varepsilon\_r$). Near the edges of the capacitor, there is a non-homogeneous electric field that causes the fluid to get polarized (that is, particles of the fluid become induced electric dipoles). One of the poles of each dipole will then be in a stronger electric field, which causes the fluid to be ''sucked'' to the inside of the capacitor (i.e. between the plates).   
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>  What's the charge $Q$, that the capacitor ought to be charged with, so that the fluid fills all space between the plates?
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Then, in my textbook, the solution is presented. This solution consists of application of the law of conservation of energy:

$$ \frac{Q^2}{2C}=\frac{Q^2}{2\varepsilon\_rC}+Sd\rho g\frac{h}{2}$$

and I find this solution absolutely wrong. Why? Consider the process of water being "sucked" into the capacitor. Then there is - inside of the capacitor - a changing electric field, that should induce changing magnetic field and so on. Therefore, I think that the solution in my textbook does not consider loss of energy due to the emitted electromagnetic waves. The answer - according to my textbook - is $$Q=S\sqrt{\frac{\varepsilon\_r\varepsilon\_0\rho gh}{\varepsilon\_r-1}}$$

Personally, I found another solution. If we compute the total energy of the system capacitor+water, and then set $\frac{dE}{dy}=0$, then we get $$Q=S\varepsilon\_r\sqrt{\frac{2\varepsilon\_0\rho gh}{\varepsilon\_r-1}}$$
which differs significantly from the solution presented in my textbook. 

Which one is the correct solution then? And, if the solution presented in my textbook does not exhibit law of conservation of energy properly, then what changes need to be made, to consider the loss of energy due to the emission of electromagnetic waves?