Explanation

The given electric field of the electromagnetic wave is

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

Comparing with the given equation, the amplitude of the electric field is

$$ E_0 = \sqrt{377}\ \text{N/C} $$

For an electromagnetic wave propagating in free space, the average power per unit area (intensity) is given by

$$ I_{\text{avg}} = \frac{E_0^2}{2Z_0} $$

where $Z_0$ is the impedance of free space and

$$ Z_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} = 377 $$

Substituting the values,

$$ I_{\text{avg}} = \frac{(\sqrt{377})^2}{2 \times 377} $$

$$ I_{\text{avg}} = \frac{377}{754} $$

$$ I_{\text{avg}} = \frac{1}{2}\ \text{W/m}^2 $$

Comparing with the given form,

$$ \frac{1}{\alpha} = \frac{1}{2} $$

$$ \alpha = 2 $$

Hence, the correct value of $\alpha$ is

$$ \boxed{2} $$

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