Discussion
If the length of a linear dipole antenna (\(l \ll \lambda\)), Ao is peak value of power density, r is radius, \(\hat{a}\) is radial unit vector, \(\theta\) is usual spherical co-ordinate, then the radiated power density is given by :
Answer: B
The radiated power density is \(\hat{a}\, A_{o} \sin^{2}\theta / r^{2}\).
For a short (Hertzian) dipole the radiated fields vary as \(\sin\theta / r\). Power density is proportional to the square of the field, so it varies as \(\sin^{2}\theta / r^{2}\), directed radially outward. With Ao defined as the peak value of the power density, it appears to the first power.
Squaring Ao would square a quantity that is already a power. A dependence on \(\sin\theta\) is that of the field, not the power, and a 1/r fall-off would also describe the field rather than the power density, which falls as the inverse square of distance.
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