Question

The velocity of electromagnetic waves in a dielectric medium(ellipslon r=4) is?

Answer 1

1.5 x 10^8 m/s

Answer 2

The velocity of electromagnetic waves in a dielectric medium is given by the formula:

$v = \frac{c}{\sqrt{\mu_r \epsilon_r}}$

Where:

• $c$ is the speed of light in vacuum ($3 \times 10^8$ m/s).
• $\mu_r$ is the relative permeability of the medium.
• $\epsilon_r$ is the relative permittivity of the medium.

For a dielectric medium, it is generally assumed to be non-magnetic, so its relative permeability $\mu_r = 1$.

Given:

• $\epsilon_r = 4$
• $c = 3 \times 10^8$ m/s

Substitute the values into the formula:

$v = \frac{3 \times 10^8}{\sqrt{1 \times 4}}$

$v = \frac{3 \times 10^8}{\sqrt{4}}$

$v = \frac{3 \times 10^8}{2}$

$v = 1.5 \times 10^8 \text{ m/s}$

The velocity of electromagnetic waves in the given dielectric medium is $1.5 \times 10^8$ m/s.

Explanation:

The velocity of electromagnetic waves in a medium is inversely proportional to the square root of the product of its relative permeability and relative permittivity. For a non-magnetic dielectric, relative permeability is 1. Substituting the given relative permittivity and the speed of light in vacuum yields the wave velocity in the medium.