# Difference between $\epsilon$ and $\epsilon_0$?

I have been given the following equation for the speed of light:

$$\V = \Large {1 \over {\sqrt {\mathstrut \epsilon \cdot \mu}}} = {1 \over \sqrt{\mathstrut \epsilon_0 \cdot \epsilon_r \cdot \mu_0 \cdot \mu_r}}\$$

What is the difference between simply $$\\epsilon\$$ and $$\\epsilon_0\$$? Likewise with $$\\mu\$$ and $$\\mu_0\$$?

• That link doesn't make much sense; "foo+bar"? Nov 30, 2020 at 14:55

What is the difference between simply epsilon and epsilon_0?

and

V = 1/sqrt(epsilon.mu) = 1/sqrt(epsilon_0.epsilon_r.mu_0.mu_r)

If you look at your formula carefully it says "epsilon_0" ($$\\epsilon_0\$$) and "epsilon_r" ($$\\epsilon_r\$$).

• $$\\epsilon_0\$$ is the absolute permittivity of free space in farads per metre. Also known as vacuum permittivity
• $$\\epsilon_r\$$ is the relative permittivity of a material with $$\\epsilon_0\$$ as the reference.

Hence, $$\\epsilon_0 \epsilon_r\$$ is the absolute permittivity of the material in farads per metre.

Likewise with mu and mu_0?

"mu" is the magnetic permeability (in henries per metre) so, it's the same principle as above but substituting $$\\mu\$$ for $$\\epsilon\$$.

So, speed of light in a medium is: -

$$c = \dfrac{1}{\sqrt{\epsilon_0 \epsilon_r \mu_0\mu_r}}$$