Intensity of electric field obtained at receiver antenna for a space wave propagation is

Options

A. directly proportional to the perpendicular-distance from transmitter to antenna
B. inversely proportional to the perpendicular-distance from transmitter to antenna
C. directly proportional to the square perpendicular distance from transmitter to antenna
D. inversely proportional to the square perpendicular distance from transmitter to antenna

Answer

To solve the question regarding the intensity of the electric field obtained at the receiver antenna for space wave propagation, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**: The intensity of the electric field at the receiver antenna is influenced by the distance between the transmitter and the receiver. In space wave propagation, the electric field strength decreases with distance.

2. **Field Strength Formula**: The intensity of the electric field \( E \) at the receiver antenna can be expressed as:
\[ E = \frac{4 \pi h h_0}{\lambda d^2} E_0 \]
where:
- \( h \) = height of the transmitter
- \( h_0 \) = height of the receiver
- \( \lambda \) = wavelength of the electromagnetic wave
- \( d \) = distance between the transmitter and the receiver
- \( E_0 \) = initial field intensity from the transmitter

3. **Analyzing the Relationship**: From the formula, we can see that the electric field intensity \( E \) is inversely proportional to the square of the distance \( d \):
\[ E \propto \frac{1}{d^2} \]

4. **Evaluating the Options**: Now, we can evaluate the given options:
- a. Directly proportional to perpendicular distance from transmitter to antenna (Incorrect)
- b. Inversely proportional to perpendicular distance from transmitter to antenna (Incorrect)
- c. Directly proportional to square of perpendicular distance from transmitter to antenna (Incorrect)
- d. Inversely proportional to square of perpendicular distance from transmitter to antenna (Correct)

5. **Conclusion**: Therefore, the correct answer is option **d**: Inversely proportional to the square of the perpendicular distance from the transmitter to the antenna.