JEE Physics 2026 Question with Solution

Given: Dielectric constant $k = 3$ and permeability $\mu = 2\mu_0$.

Find: The ratio of speed of electromagnetic waves in vacuum to that in the medium.

For electromagnetic waves,

$$v = \frac{1}{\sqrt{\epsilon \mu}}$$

In vacuum,

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

Since dielectric constant

$$k = \frac{\epsilon}{\epsilon_0} = 3$$

we get

$$\epsilon = 3\epsilon_0$$

Also,

$$\mu = 2\mu_0$$

So the speed in the medium is

$$v_m = \frac{1}{\sqrt{\epsilon \mu}} = \frac{1}{\sqrt{3\epsilon_0 \cdot 2\mu_0}} = \frac{1}{\sqrt{6\epsilon_0 \mu_0}}$$

Therefore,

$$\frac{c}{v_m} = \frac{1/\sqrt{\epsilon_0 \mu_0}}{1/\sqrt{6\epsilon_0 \mu_0}} = \sqrt{6}$$

Hence, the required ratio is $\sqrt{6}:1$. The correct option is A.

Given: Relative permittivity $\epsilon_r = 3$ and relative permeability $\mu_r = 2$.

Find: The ratio of speeds in vacuum and medium.

Use the relation

$$n = \sqrt{\epsilon_r \mu_r}$$

Thus,

$$n = \sqrt{3 \times 2} = \sqrt{6}$$

Since refractive index

$$n = \frac{c}{v_m}$$

we get

$$\frac{c}{v_m} = \sqrt{6}$$

Therefore, the ratio is $\sqrt{6}:1$. The correct option is A.