The power radiated by linear antenna of length 'l' is proportional to (`lambda`=wavelength)

Options

A. `Pprop(l/lamda)`
B. `Pprop(lamda/l)^2`
C. `Pprop(l/lamda)^2`
D. `Pprop(lamda/l)`

Answer

To solve the question regarding the power radiated by a linear antenna of length 'l' and its relationship with wavelength (λ), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The power radiated by an antenna is influenced by its physical dimensions and the characteristics of the waves it emits. We need to establish how the length of the antenna (L) and the wavelength (λ) relate to the power (P) radiated.

2. **Proportionality of Power to Length**:
It is known from electromagnetic theory that the power radiated by a linear antenna is proportional to the square of its length. This can be expressed mathematically as:
\[ P \propto L^2 \]

3. **Proportionality of Power to Wavelength**:
Additionally, the power radiated is inversely proportional to the square of the wavelength. This can be expressed as:
\[ P \propto \frac{1}{\lambda^2} \]

4. **Combining the Relationships**:
By combining the two relationships, we can express the power radiated by the antenna in terms of both its length and wavelength:
\[ P \propto \frac{L^2}{\lambda^2} \]

5. **Final Expression**:
To express this in a single proportionality statement, we can write:
\[ P \propto \frac{L^2}{\lambda^2} \implies P \propto \frac{L}{\lambda^2} \]
This indicates that the power radiated is directly proportional to the length of the antenna and inversely proportional to the square of the wavelength.

6. **Conclusion**:
Therefore, the correct answer to the question is that the power radiated by a linear antenna of length 'l' is proportional to:
\[ P \propto \frac{L}{\lambda^2} \]