Speed Of Electromagnetic Waves

One of Maxwell's most celebrated results is that the speed of electromagnetic waves in vacuum depends only on two electric and magnetic constants, through c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}. Computing the product, \mu_0 \varepsilon_0 = (1.2566 \times 10^{-6})(8.85 \times 10^{-12}) = 1.112 \times 10^{-17}\ \text{s}^2/\text{m}^2. Taking the reciprocal square root, c = 1/\sqrt{1.112 \times 10^{-17}} = 3.0 \times 10^{8}\ \text{m/s}. The 1.5 \times 10^{8}\ \text{m/s} option would be the speed in a medium of refractive index 2, not vacuum. The 9.0 \times 10^{16}\ \text{m/s} value forgets to take the square root and is the value of c^2. The 3.0 \times 10^{6}\ \text{m/s} answer is off by two powers of ten. The remarkable closeness of this computed speed to the measured speed of light convinced Maxwell that light itself is an electromagnetic wave, a cornerstone of the NCERT chapter. What makes the result so profound is that neither \mu_0 nor \varepsilon_0 was originally measured using light at all; one comes from magnetic force experiments and the other from electrostatics, yet together they reproduce the optical speed exactly. This unexpected meeting of electricity, magnetism, and optics is precisely why the prediction was historically decisive. As a check, the answer matches the well-known value of c to within rounding, confirming the calculation.