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GATE EC 2014 Set 1 — Question 63

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NAT+2 / -0MediumPoynting Vector & Power FlowMaxwell's EquationsElectromagneticsDipole & Monopole AntennasAntennas

Electromagnetics → Antennas → Dipole & Monopole Antennas

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Question

In spherical coordinates, let a^θ,a^ϕ\hat{a}_\theta, \hat{a}_\phi denote unit vectors along the θ,ϕ\theta, \phi directions.E=100rsin⁡θcos⁡(ωt−βr)a^θV/m\mathbf{E} = \frac{100}{r} \sin \theta \cos(\omega t - \beta r) \hat{a}_\theta V/mandH=0.265rsin⁡θcos⁡(ωt−βr)a^ϕA/m\mathbf{H} = \frac{0.265}{r} \sin \theta \cos(\omega t - \beta r) \hat{a}_\phi A/mrepresent the electric and magnetic field components of the EM wave at large distances rr from a dipole antenna, in free space. The average power (W) crossing the hemispherical shell located at r=1km,0≤θ≤π/2r = 1km, 0 \leq \theta \leq \pi/2 is ________
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