Distance of propogation from antenna of height 20m is

Options

A. 80km
B. 8km
C. 16km
D. 6.8km

Answer

To find the distance of propagation from an antenna of height 20m, we can use the formula for the range of an antenna.

### Step-by-Step Solution:

1. **Identify the Formula**:
The formula for the range (distance of propagation) of an antenna is given by:
\[ R = \sqrt{2 \cdot R_e \cdot h_t} \]
where:
- \( R \) is the range,
- \( R_e \) is the radius of the Earth (approximately \( 6.4 \times 10^6 \) meters),
- \( h_t \) is the height of the antenna.

2. **Substitute the Values**:
Given:
- Height of the antenna \( h_t = 20 \) m,
- Radius of the Earth \( R_e = 6.4 \times 10^6 \) m.

Plugging these values into the formula:
\[ R = \sqrt{2 \cdot (6.4 \times 10^6) \cdot 20} \]

3. **Calculate the Product Inside the Square Root**:
First, calculate the product:
\[ 2 \cdot 6.4 \times 10^6 \cdot 20 = 256 \times 10^6 \]

4. **Take the Square Root**:
Now, take the square root of \( 256 \times 10^6 \):
\[ R = \sqrt{256 \times 10^6} = \sqrt{256} \times \sqrt{10^6} = 16 \times 10^3 = 16000 \text{ m} \]

5. **Convert to Kilometers**:
To convert meters to kilometers, divide by 1000:
\[ R = \frac{16000}{1000} = 16 \text{ km} \]

### Final Answer:
The distance of propagation from the antenna of height 20m is **16 km**.