In a region where intensity of electric field is `5NC^(-1)40` lines of electric force are crossing per square metre. The number of lines crossing per square metre where intensity of electric field is `10NC^(-1)` will be

Options

A. 20
B. 80
C. 100
D. 200

Explanation

To solve the problem, we need to understand the relationship between the electric field intensity (E) and the number of electric field lines crossing a unit area (which we can consider as electric flux, φ).

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- We have an electric field intensity \( E_1 = 5 \, \text{N/C} \).
- The number of electric field lines crossing per square meter at this intensity is \( \phi_1 = 40 \, \text{lines/m}^2 \).
- We need to find the number of lines crossing per square meter when the electric field intensity is \( E_2 = 10 \, \text{N/C} \).

2. **Using the Relationship Between Electric Field and Electric Flux**:
- The number of electric field lines (or electric flux) is directly proportional to the electric field intensity. This can be expressed as:
\[ \frac{\phi_1}{\phi_2} = \frac{E_1}{E_2} \]
- Rearranging this gives:
\[ \phi_2 = \phi_1 \cdot \frac{E_2}{E_1} \]

3. **Substituting the Known Values**:
- We know:
- \( \phi_1 = 40 \, \text{lines/m}^2 \)
- \( E_1 = 5 \, \text{N/C} \)
- \( E_2 = 10 \, \text{N/C} \)
- Substituting these values into the equation:
\[ \phi_2 = 40 \cdot \frac{10}{5} \]

4. **Calculating \( \phi_2 \)**:
- Simplifying the right-hand side:
\[ \phi_2 = 40 \cdot 2 = 80 \, \text{lines/m}^2 \]

5. **Final Answer**:
- The number of lines crossing per square meter where the intensity of the electric field is \( 10 \, \text{N/C} \) is \( 80 \, \text{lines/m}^2 \).