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

Options

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

Explanation

To solve the problem of determining how the power radiated by a linear antenna of length 'l' is related to the wavelength (λ), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The problem states that the power radiated (P_r) by a linear antenna is proportional to its length (l) and inversely proportional to the wavelength (λ). This can be expressed mathematically as:
\[ P_r \propto \frac{l}{\lambda^2} \]

2. **Expressing the Proportionality**:
To convert the proportionality into an equation, we can introduce a constant of proportionality (k):
\[ P_r = k \cdot \frac{l}{\lambda^2} \]

3. **Analyzing the Options**:
We have four options to choose from:
- Option 1: \(\frac{\lambda}{l}\)
- Option 2: \(\frac{\lambda l}{l^2}\)
- Option 3: \(\frac{l}{l^2}\)
- Option 4: \(\frac{l}{\lambda^2}\)

4. **Identifying the Correct Option**:
From our derived equation \(P_r = k \cdot \frac{l}{\lambda^2}\), we see that the correct relationship matches Option 4:
\[ P_r \propto \frac{l}{\lambda^2} \]

5. **Conclusion**:
Therefore, the correct answer is:
\[ \text{Option 4: } \frac{l}{\lambda^2} \]