Discussion
The far field pattern of a half wave dipole is \( \cos(\tfrac{\pi}{2}\cos\theta)/\sin\theta \). What is its value along the wire axis?
Answer: B
Setting theta to zero makes the cosine argument pi over two, whose cosine is zero, and although the denominator also vanishes the limit is zero:
\[ \lim_{\theta \to 0} F(\theta) = 0 \]
so there is a null along the wire. The pattern is maximum broadside at ninety degrees, where the function equals one. Every linear current distribution shares this axial null, which is why a vertical dipole radiates nothing straight up.
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