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In spherical coordinates, let $\hat{a_{\theta}},\hat{a_{\phi}}$ denote unit vectors along the $\theta,\phi$ directions.

$$\textbf{E} = \dfrac{100}{r}\sin\theta \cos (\omega t – \beta r)\hat{a_{\theta}}\: V/m$$

and

$$\textbf{H} = \dfrac{0.265}{r}\sin\theta \cos (\omega t – \beta r)\hat{a_{\phi}} \:A/m$$

represent the electric and magnetic field components of the EM wave at large distances $r$ from a dipole antenna, in free space. The average power $(W)$ crossing the hemispherical shell located at $r = 1\:km,0\leq \theta \leq \pi/2$ is ______.
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