Statement1: The magnetic filed at the ends of very long current carrying solenoid is half of that at the centre.
Statement2: If the solenoid is sufficiently long, the field within it is uniform.

Options

A. If both Statement 1 and Statement 2 are true, the Statement 2 is the correct explanation of Statement1.
B. If both Statement 1 and Statement 2 are true, Statement 2 is not the correct explanation of Statement 1.
C. If Statement 1 is true, Statement 2 is false.
D. If Statement 1 is false, Statement 2 is true.

Explanation

To analyze the statements regarding the magnetic field in a long current-carrying solenoid, let's break down the concepts involved step by step.

### Step 1: Understanding the Magnetic Field Inside a Solenoid
A solenoid is a long coil of wire that generates a magnetic field when an electric current passes through it. The magnetic field inside a long solenoid is given by the formula:
\[ B = \mu_0 \frac{N}{L} I \]
where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space,
- \( N \) is the number of turns of the coil,
- \( L \) is the length of the solenoid,
- \( I \) is the current flowing through the solenoid.

### Step 2: Magnetic Field at the Center of the Solenoid
For a sufficiently long solenoid, the magnetic field is uniform throughout its length, and its strength is maximum at the center. Thus, we can denote the magnetic field at the center of the solenoid as \( B_{\text{center}} \).

### Step 3: Magnetic Field at the Ends of the Solenoid
At the ends of the solenoid, the magnetic field is not as strong as it is at the center. In fact, it can be shown that the magnetic field at the ends of a long solenoid is approximately half of that at the center:
\[ B_{\text{end}} \approx \frac{1}{2} B_{\text{center}} \]

### Step 4: Evaluating Statement 1
Statement 1 claims that "The magnetic field at the ends of a very long current-carrying solenoid is half of that at the center." This statement is true based on the analysis above.

### Step 5: Evaluating Statement 2
Statement 2 states, "If the solenoid is sufficiently long, the field within it is uniform." This statement is also true. A sufficiently long solenoid does produce a uniform magnetic field inside it.

### Step 6: Analyzing the Relationship Between the Statements
While both statements are true, Statement 2 does not provide a direct explanation for Statement 1. Statement 1 specifically describes the relationship between the magnetic field strengths at the ends and the center of the solenoid, while Statement 2 describes the uniformity of the field within the solenoid.

### Conclusion
Both statements are true, but Statement 2 is not a proper explanation for Statement 1. Therefore, the correct conclusion is that both statements are true, but the second statement does not explain the first.

### Final Answer
Both Statement 1 and Statement 2 are true, but Statement 2 is not the correct explanation of Statement 1.

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