Question

An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of the 6 dB gain (rounded off to three decimal places) is V/m.

Hint:

The electric field strength at a distance from the antenna can be found using the formula \( E = \sqrt{\frac{P \cdot \eta}{r^2}} \), where \( r \) is the distance from the antenna.

Answer 1

Correct Answer: 0.224

The power radiated by the antenna is related to the electric field strength by the formula: \[ P = \frac{E^2}{\eta} \] where \( \eta \) is the intrinsic impedance of free space (\( \eta = 377 \, \Omega \)) and \( P = 16 \, \text{kW} = 16000 \, \text{W} \). The electric field at the distance \( r = 8 \, \text{km} \) is: \[ E = \sqrt{P \cdot \eta} \] Substituting the given values: \[ E = \sqrt{16000 \times 377} \approx 0.224 \, \text{V/m} \] Thus, the electric field is \( \boxed{0.224} \, \text{V/m} \).