The self inductance of a long solenoid cannot be increased by

Options

A. increasing its area of corss section
B. decreasing its length
C. increasing the current through it
D. increasing the number of turns in it

Explanation

To solve the question regarding the self-inductance of a long solenoid, we need to analyze the formula for self-inductance and how it can be affected by various factors.

### Step-by-Step Solution:

1. **Understand the Formula for Self-Inductance**:
The self-inductance \( L \) of a long solenoid is given by the formula:
\[ L = \frac{\mu_0 N^2 A}{l} \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( N \) is the number of turns,
- \( A \) is the cross-sectional area,
- \( l \) is the length of the solenoid.

2. **Analyze Each Option**:
We will evaluate how each option affects the self-inductance \( L \).

- **Increasing the Area of Cross-Section \( A \)**:
If we increase the area \( A \), the self-inductance \( L \) increases because \( L \) is directly proportional to \( A \).

- **Decreasing the Length \( l \)**:
If we decrease the length \( l \), the self-inductance \( L \) increases because \( L \) is inversely proportional to \( l \).

- **Increasing the Current \( I \)**:
The formula for self-inductance does not include \( I \). Therefore, increasing the current through the solenoid does not affect the self-inductance \( L \).

- **Increasing the Number of Turns \( N \)**:
If we increase the number of turns \( N \), the self-inductance \( L \) increases because \( L \) is directly proportional to \( N^2 \).

3. **Conclusion**:
From the analysis above, the self-inductance of a long solenoid cannot be increased by **increasing the current through it**. This is the correct answer.

### Final Answer:
The self-inductance of a long solenoid cannot be increased by **increasing the current through it**.

---