The number of electric field lines crossing an area `DeltaS is n_1 when Delta vecS||vecE`, while the number of field lines crossing the same area is `n_2` when `DeltavecE` makes an angles of `30^@` with `vecE`. Then

Options

A. `n_1 = n_2`
B. `n_1gtn_2`
C. `n_1`lt`n_2`
D. cannot say anything

Explanation

To solve the problem, we need to relate the number of electric field lines crossing an area when the area is aligned with the electric field and when it is at an angle to the electric field.

### Step-by-Step Solution:

1. **Understanding Electric Flux**:
Electric flux (Φ) through a surface is defined as the product of the electric field (E) and the area (ΔS) through which the field lines pass, taking into account the angle (θ) between the electric field and the normal to the surface. Mathematically, this is given by:
\[ \Phi = E \cdot \Delta S \cdot \cos(\theta) \]

2. **Case 1 - Area Parallel to Electric Field**:
When the area ΔS is parallel to the electric field (θ = 0°), the electric flux (Φ₁) is maximized:
\[ \Phi_1 = E \cdot \Delta S \cdot \cos(0°) = E \cdot \Delta S \cdot 1 = E \cdot \Delta S \]
The number of electric field lines crossing the area in this case is denoted as \( n_1 \).

3. **Case 2 - Area at 30° to Electric Field**:
When the area ΔS makes an angle of 30° with the electric field, the electric flux (Φ₂) is given by:
\[ \Phi_2 = E \cdot \Delta S \cdot \cos(30°) = E \cdot \Delta S \cdot \frac{\sqrt{3}}{2} \]
The number of electric field lines crossing the area in this case is denoted as \( n_2 \).

4. **Comparing n₁ and n₂**:
From the expressions for electric flux, we can relate the number of electric field lines:
\[ n_1 = E \cdot \Delta S \]
\[ n_2 = E \cdot \Delta S \cdot \frac{\sqrt{3}}{2} \]

5. **Finding the Relationship**:
To compare \( n_1 \) and \( n_2 \):
\[ n_2 = n_1 \cdot \frac{\sqrt{3}}{2} \]
Since \( \frac{\sqrt{3}}{2} \) is approximately 0.866, it follows that:
\[ n_2 < n_1 \]

6. **Conclusion**:
Therefore, the relationship between the number of electric field lines is:
\[ n_1 > n_2 \]

### Final Answer:
The correct relationship is \( n_1 > n_2 \).

---