Yes, absolutely. And a key thing about that is that Maxwell's Equations can be written in the same mathematical form as the equations that describe waves - wave equations. And when that is done, the term that (if they were describing waves) would indicate the speed of the waves is the combinations of ε0 and μ0 as you've said. When this was discovered, the values of ε0 and μ0 as measured by experiments such as those carried out by Faraday gave a value for this speed term equal to the speed of light, as measured by other means.Frewah wrote:...The point is that ε and μ are the fundamental properties from which c can be derived.
So this is a classic example of the power of physics to unite phenomena that are previously apparently unrelated. In this case its the strengths of the electric and magnetic fields united together with the speed of light. Who would have thought that experiments involving measuring the size of the forces between magnets and the size of the forces between electrical charges would yield the speed of light! Measured by such means as observing the orbits of the moons of Jupiter. And then, via Special Relativity, the electric and magnetic forces themselves are united (into the single phenomenon of electromagnetism) by observing that magnetism is a relativistic manifestation of the electric force.
The magnetic force is the electric force when the principle of relativity is taken into account.
But a key thing about the discovery that the speed of light emerges from Maxwell's equations (as you've said) is that it emerges as a physical constant. By definition, the concepts of speed and velocity only make sense when we specify what we're measuring that velocity relative to. But the term for 'c' that emerges from Maxwell's Equations, when seen as the speed of electromagnetic waves, doesn't tell us what that speed is measured against. What it does tell us, if Maxwell's equations are valid (as Faraday's experiments suggest that they are) is that the speed will be measured as constant by any observer, in the same way that the values of ε0 and μ0 are measured as constant by any experimenter. And it's that fact, when its implications were considered very carefully, that led to Special Relativity.