Assertion : The self-inductionce of a long solenoid is proportional to the area of corss-section and length of the solenoid.
Reason : Self inductance of a solenoid is independent of the number of truns per unit length.

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided in the context of self-inductance of a long solenoid.

**Step 1: Understanding the Assertion**
The assertion states that "The self-inductance of a long solenoid is proportional to the area of cross-section and length of the solenoid."

- The formula for the self-inductance \( L \) of a solenoid is given by:
\[ L = \mu_r \mu_0 \frac{N^2 A}{l} \]
where:
- \( \mu_r \) is the relative permeability of the core,
- \( \mu_0 \) is the permeability of free space,
- \( N \) is the total number of turns,
- \( A \) is the cross-sectional area,
- \( l \) is the length of the solenoid.

From the formula, we can see that \( L \) is directly proportional to the area \( A \) and the length \( l \). Thus, the assertion is **true**.

**Step 2: Understanding the Reason**
The reason states that "Self-inductance of a solenoid is independent of the number of turns per unit length."

- However, from the formula, we can see that \( L \) is actually dependent on the number of turns per unit length \( n \) (which is \( N/l \)). The self-inductance increases with the square of the number of turns per unit length. Therefore, the reason is **false**.

**Step 3: Conclusion**
Now, we can summarize our findings:
- The assertion is true.
- The reason is false.
- Since the reason does not correctly explain the assertion, the answer to the question is that the assertion is true, but the reason is false.

Thus, the final answer is **Option C**: The assertion is true, and the reason is false.

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