1. Speed of electromagnetic waves in a medium

   The speed of an electromagnetic wave in a medium is $v = \frac{c}{\sqrt{\mu_r \varepsilon_r}}$ where:

   • $v = 2.0 \times 10^8\ \text{m/s}$
   • $c = 3.0 \times 10^8\ \text{m/s}$
   • $\mu_r = 1.0$
   • $\varepsilon_r = ?$

2. Substitute the given values

   $2.0 \times 10^8 = \frac{3.0 \times 10^8}{\sqrt{1 \cdot \varepsilon_r}}$

   Cancelling $10^8$: $2 = \frac{3}{\sqrt{\varepsilon_r}}$

3. Solve for $\varepsilon_r$

   $\sqrt{\varepsilon_r} = \frac{3}{2}$

   Squaring both sides: $\varepsilon_r = \left(\frac{3}{2}\right)^2 = \frac{9}{4} = 2.25$

4. Check options

   • A: $2.25$ ✅
   • B: $4.25$
   • C: $6.25$
   • D: $8.25$

Therefore, the correct answer is A.