Speed of Light from two Other Variables

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Mockingbird students found this:

speed of light in a vacuum = \dfrac {1}{ \sqrt { \epsilon_0 \mu_0}}

Pieces of their “chickenscratch” are provided below. Can you put the pieces together to get the speed of light?

  • \mu_0 – Vacuum Permeability
  • \epsilon_0 – Vacuum Permittivity

  • \epsilon_0 = 8.8541878128 x 10^{-12} \dfrac {F}{m}
  • \mu_0 = 1.256637062 x 10^{-6}\dfrac {H}{m}

\mu_0 \epsilon_0 = 1.112650056 x 10^{-17} \dfrac {H F} {m^2}

\dfrac {1}{ \sqrt{1.113650056 x 10^{-17}}} = 2.99792458 x 10^7

Units

1H = 1 \dfrac {kg m^2}{s^2 A^2}

1 F = 1 \dfrac {s^4 A^2}{m^2 kg}

\dfrac {kg m^2}{s^2 A^2} \dfrac {s^4 A^2}{m^2 kg} = \dfrac {s^2} {1}

\dfrac {H F}{m^2} = \dfrac {s^2}{m^2}

Appendix A

There’s a reason they make a big deal about it being speed in a vacuum. Light can travel through a material and the result is, we calculate a speed that is less than the number shown above. The explanation for this is kind of like a person driving a hundred kilometers per hour on the turnpike but at every rest stop they stop for 10 minutes and so when they’re done driving across the turnpike, the calculation of distance traveled divided by time will give you a number less than a hundred.

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Published by Robert Sterling

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