Mutual capacitance upper limit I am having trouble making an analog for mutual capacitance from mutual inductance. In circuits with magnetic coupling, there is an upper limit established on mutual inductance due to energy conservation principles: 
$M \leq \sqrt{L_1 * L_2} $
Where $L_1$ and $L_2$ are the two coupled inductors. 
This makes sense intuitively as well because the mutual inductance represents magnetic flux generated by one inductor and coupling with another, and you can't share more flux than is produced by a single inductor. It seems like a similar relationship would hold for Mutual Capacitance, but I can believe there should be a case where the mutual capacitance between two components is greater than the geometric mean of their respective capacitances... 
Does anyone know of an energy bound upper limit for mutual capacitance? Thank you in advance and I apologize if my question is poorly formed, most of my confusion comes from reconciling circuit interpretations of mutual capacitance and the physics of how the mutual capacitance is manifested. 
 A: Yes, there is a constraint also for the mutual capacitance. As I shortly reviewed in this answer, the capacitance matrix of a system of conductors is a symmetric and positive definite matrix, exactly as the inductance matrix of a system of inductors. Since the relationship $M\le \sqrt{L_1L_2}$ can be directly obtained from this property, which, in turns can be derived from the conservation of energy, it's not difficult to prove the analogue for a system of three conductors where one is taken as reference conductor (ground).
Consider the system of two conductors with ground shown below (beware the sign of $C_{12}$: what you called "mutual capacitance" is actually $-C_{12}$, $C_{12}=C_{21}$ being the off-diagonal element of the capacitance matrix):

For such a system, the capacitance matrix is a 2-by-2 symmetric matrix with $C_{11} = C_1-C_{12}$, $C_{22} = C_2-C_{12}$ and $C_{12}<0$ ($C_{11}$ and $C_{22}$ are the total capacitances from each conductor to the other conductors). Such a matrix is further positive definite if and only if its trace and determinant are positive (see e.g. this question on Math SE). From the condition on the determinant, we thus have
$$C_{11}C_{22}-C_{12}^2\ge 0,$$
that is,
$$|C_{12}|\le\sqrt{C_{11}C_{22}}.$$
For further details and derivations for the general case, see:
R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic fields, energy, and forces, MIT Press, 1968.
A: I think you're drawing a parallel where none exists. Mutual inductance is where a changing current in one inductor influences the current in an adjacent inductor; this happens because it's easy for the (also changing) magnetic field of one inductor goes through another inductor (e.g. a transformer).
Mutual capacitance, instead, is just a measure of the capacitive coupling between two objects when treating the two objects as a single capacitor. You could imagine two separate capacitors coupling, but it's hard to design two capacitors such that their electrical fields influence each other, as the vast majority of each capacitor's field's energy is between its two conductors.
