The self inductance of a long solenoid cannot be increased by

Options

A. increasing its area of cross-section
B. increasing its length
C. changing the medium with greater permeability
D. increasing the current through it

Explanation

To solve the question regarding the self-inductance of a long solenoid and how it cannot be increased, we can follow these steps:

### Step 1: Understand the formula for self-inductance
The self-inductance \( L \) of a solenoid is given by the formula:
\[ L = \mu \frac{N^2 A}{l} \]
where:
- \( \mu \) = permeability of the medium inside the solenoid,
- \( N \) = number of turns of the solenoid,
- \( A \) = cross-sectional area of the solenoid,
- \( l \) = length of the solenoid.

### Step 2: Analyze each option
1. **Increasing its area of cross-section**:
- From the formula, we see that \( L \) is directly proportional to the area \( A \). Therefore, increasing the area will increase the self-inductance. This option does not answer the question.

2. **Increasing its length**:
- The formula shows that \( L \) is inversely proportional to the length \( l \). Thus, increasing the length will decrease the self-inductance. This option does not answer the question either.

3. **Changing the medium with greater permeability**:
- The self-inductance \( L \) is directly proportional to the permeability \( \mu \). Therefore, using a medium with greater permeability will increase the self-inductance. This option does not answer the question.

4. **Increasing the current through the solenoid**:
- The self-inductance \( L \) is independent of the current flowing through the solenoid. Therefore, increasing the current will not affect the self-inductance. This is the correct answer to the question.

### Conclusion
The self-inductance of a long solenoid cannot be increased by **increasing the current through the solenoid**.

### Final Answer
The correct option is: **Increasing the current through the solenoid**.

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