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## Can the Speed of Light be derived?

Well, historically Maxwell used his newly-corrected Ampere law to get an electromagnetic wave equation. When solving this equation, he found that EM waves travel at a speed given by:

$v=\frac{1}{\sqrt{\mu_0 \epsilon _0}}$

, where μ0 and ε0 are the magnetic and electric constants. When he calculated this value, he found that it was the same speed that light was known to travel at, suggesting that light consisted of EM waves.