The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 10⁸ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

The speed of electromagnetic waves in a medium is given by the formula: <br/><br/>$v = \frac{1}{\sqrt{\mu \varepsilon}}$ <br/><br/>where $\mu$ and $\varepsilon$ are the absolute permeability and absolute permittivity of the medium, respectively. <br/><br/>Given that $\mu = \mu_0 \mu_r$ and $\varepsilon = \varepsilon_0 \varepsilon_r$, we can rewrite the above equation as : <br/><br/>$v = \frac{1}{\sqrt{\mu_0 \mu_r \varepsilon_0 \varepsilon_r}}$ <br/><br/>which simplifies to : <br/><br/>$$v = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \times \frac{1}{\sqrt{\mu_r \varepsilon_r}}$$ <br/><br/>Substituting $c$ for $\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ (the speed of light in a vacuum), we get: <br/><br/>$v = \frac{c}{\sqrt{\mu_r \varepsilon_r}}$ <br/><br/>We can rearrange this equation to solve for $\varepsilon_r$ : <br/><br/>$$\varepsilon_r = \frac{c^2}{v^2 \mu_r} = \frac{(3 \times 10^8 m/s)^2}{(2 \times 10^8 m/s)^2 \times 1} = 2.25$$ <br/><br/>So, the relative permittivity of the medium is 2.25.