Explanation

The given equation represents a plane electromagnetic wave of the form:

$$ E = E_0 \sin (kx - \omega t) $$

From the given equation:

$$ k = 3 \times 10^6\ \text{rad/m} $$

$$ \omega = 4.5 \times 10^{14}\ \text{rad/s} $$

The speed of the electromagnetic wave in the medium is:

$$ v = \frac{\omega}{k} $$

$$ v = \frac{4.5 \times 10^{14}}{3 \times 10^6} = 1.5 \times 10^8\ \text{m/s} $$

For a nonmagnetic medium:

$$ v = \frac{c}{\sqrt{K}} $$

where $K$ is the dielectric constant of the medium.

$$ \sqrt{K} = \frac{c}{v} = \frac{3 \times 10^8}{1.5 \times 10^8} = 2 $$

$$ K = 4 $$

Hence, the dielectric constant of the medium is:

4

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