Question

According to theoretical study of radiation from the same linear antenna, the power radiated is proportional to ( \( \lambda \) = wavelength )

• A. \( \lambda^{-2} \)
• B. \( \lambda^{-1} \)
• C. \( \lambda^{2} \)
• D. \( \lambda \)

Hint:

For antennas of fixed size, higher frequency (shorter wavelength) radiation leads to greater power emission.

Answer 1

The Correct Option is A

Step 1: Recall radiation from a linear antenna.
For a linear (Hertzian) antenna of fixed length, the power radiated depends on the frequency of the emitted electromagnetic waves.
Step 2: Relation between power and frequency.
The radiated power is proportional to the square of frequency: \[ P \propto \nu^2 \]
Step 3: Use relation between frequency and wavelength.
\[ \nu = \frac{c}{\lambda} \Rightarrow \nu^2 \propto \frac{1}{\lambda^2} \]
Step 4: Substitute in power relation.
\[ P \propto \frac{1}{\lambda^2} \]
Step 5: Conclusion.
The power radiated is proportional to \( \lambda^{-2} \).