Question

Find the power radiated from the half wave dipole at 2km away with magnetic field at point \(\theta=\frac{\pi}{2}\) is 10μA/m ?

(a) 0.576mW

(b) 0.576W

(c) 0.756W

(d) 0.675W

The question was asked in an online quiz.

The doubt is from Power Radiation from Half Wave Dipole in portion Antenna Parameters – II of Antennas

Answer 1

The correct answer is (b) 0.576W

Easy explanation: Magnetic field strength \(H=\frac{I_m}{2\pi r}(\frac{cos⁡(\frac{\pi}{2}cos\theta)}{sin\theta})\)

⇨ 10×10^-6=\(\frac{I_m}{2\pi×2×10^3}(\frac{cos⁡(\frac{\pi}{2}cos\frac{\pi}{2})}{sin\frac{\pi}{2}})\)

⇨ Im=0.125A

Now Average power radiated \(P_{avg}=I_{rms}^2 R=(\frac{I_m}{\sqrt 2})^2 R=(\frac{0.125}{\sqrt 2})^2 ×73×=0.576W\)