Speed of Light (EM)
Light speed from vacuum constants.
Formula
Variables
Example
≈ 3×10⁸ m/s
How it works
This formula says that electromagnetic waves travel through empty space at a speed fixed entirely by two vacuum properties: how strongly space permits electric fields to form (b5) and how strongly it permits magnetic fields (bc). It comes directly from Maxwell's equations: changing electric fields create magnetic fields, and changing magnetic fields create electric fields, so the coupled waves propagate with speed 1/\sqrt{\mu_0\varepsilon_0}. The result is the vacuum speed of light, showing that light is an electromagnetic wave.
When to use it
Use this when you need the propagation speed of an electromagnetic wave in vacuum, or when relating fundamental constants in electromagnetism. It is also useful in advanced optics, wave physics, and derivations connecting Maxwell's equations to the speed of light.
Worked example, step by step
Given: \mu_0 = 4\pi \times 10^{-7}\ \text{H/m}, \varepsilon_0 = 8.854 \times 10^{-12}\ \text{F/m} Step 1: Multiply the constants \mu_0\varepsilon_0 = (4\pi \times 10^{-7})(8.854 \times 10^{-12}) \approx 1.112 \times 10^{-17} Step 2: Take the square root \sqrt{\mu_0\varepsilon_0} = \sqrt{1.112 \times 10^{-17}} \approx 3.33 \times 10^{-9} Step 3: Invert to get the speed c = \frac{1}{3.33 \times 10^{-9}} \approx 3.00 \times 10^8\ \text{m/s} Final answer: c \approx 3.00 \times 10^8\ \text{m/s}
Common mistakes to avoid
- Using this formula for light in matter instead of vacuum, where the speed is lower.
- Forgetting that the result is the same constants in SI units; mixing unit systems gives the wrong value.
- Confusing c with a derived wave speed in a medium, which depends on material properties and not just \u03bc\u00f0 and \u03b5\u00f0.
Did You Know?
Maxwell computed light's speed purely from electric and magnetic constants, proving light is an electromagnetic wave.
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