Is there any correlation between mass-energy equivalence and Maxwell's 4th equation? I wonder, how came in both equations proportionality constant is exactly $c^2$?
$$c^2(\nabla \times B) = \partial E/\partial t$$ 
where $E$ - electric field
$$c^2m = E$$
where $E$ - energy
I am just curious can we relate these two equations. 
 A: The correlation is the Special Relativity itself. It connects some different physical values to each other and elucidates them as being spatial and temporal counterparts of one unified value, which "lives" in the space-time being indifferent to the particular space and time aspects. From this point of view, we have better correct our unit measures, so they would be the same for each counterpart. This is done by the $c$ constant, which works purely as a correction factor. (Example: we can measure time in seconds, and distance in light seconds which are $c\cdot(1\text{ second})$ long.) Since SR affects all physical phenomena and theories, the factors $c^n$ appear everywhere in formulas. Any SR textbook could provide you with many more examples.
A: Electromagnetic field has energy density, and has momentum. According to relativity, rest inertial mass has a strict relationship with energy and momentum magnitudes as a conic-shell invariant
$$ m^2 c^4 = E^2 - c^2 P^2$$
So this allows the possibility of defining inertia for an electromagnetic field. Look at eq.(5) in this paper: http://arxiv.org/abs/1105.4834 for a derivation. 
The reason that there is a $c^2$ in Maxwell equation should not surprise you. As you know, combining Maxwell equations you can obtain a wave equation for the electromagnetic field. Wave equations have the property that the constant accompanying second derivative of time is just the inverse square of the wave speed. This constant can be related to the vacuum permittivity and susceptibility.
