If there is one hollow metallic tube which carries current uniformly distributed over its surface, which of the statements is correct?

Options

A. Magnetic field intensity inside the tube remains constant, and it is not zero.
B. Magnetic field intensity inside the tube is same as its value on surface.
C. Magnetic field is zero everywhere inside the tube.
D. Magnetic field for points outside is same as magnetic field produced by a straight wire kept along the axis of tube.

Explanation

To solve the problem regarding the magnetic field produced by a hollow metallic tube carrying a uniformly distributed current, we can analyze each statement given in the question step by step.

### Step 1: Understanding the Configuration
We have a hollow metallic tube with a current \( I \) uniformly distributed over its surface. We need to analyze the magnetic field inside and outside the tube.

### Step 2: Magnetic Field Inside the Tube
Using Ampere's Circuital Law, we can analyze the magnetic field inside the tube. According to Ampere's Law:
\[ \oint \mathbf{B} \cdot d\mathbf{L} = \mu_0 I_{\text{enc}} \]
Where \( I_{\text{enc}} \) is the current enclosed by the Amperian loop.

- Inside the hollow tube, there is no current enclosed because the current flows only on the surface. Therefore, \( I_{\text{enc}} = 0 \).
- This implies:
\[ \oint \mathbf{B} \cdot d\mathbf{L} = 0 \implies B = 0 \text{ inside the tube} \]

### Step 3: Evaluating the Statements
1. **Statement 1**: "Magnetic field intensity inside the tube remains constant and it is not zero."
- **Conclusion**: Incorrect, as we found that the magnetic field inside the tube is zero.

2. **Statement 2**: "Magnetic field intensity inside the tube is same and its value on the surface."
- **Conclusion**: Incorrect, as the magnetic field inside the tube is zero, while the surface has a non-zero magnetic field.

3. **Statement 3**: "Magnetic field is zero everywhere inside the tube."
- **Conclusion**: Correct, as we established that the magnetic field inside the tube is indeed zero.

4. **Statement 4**: "Magnetic field for points outside is same as magnetic field produced by a straight wire kept along the axis of tube."
- **Conclusion**: Correct, as the magnetic field outside the tube behaves like that of a straight wire carrying the same current.

### Final Answers
- The correct statements are **Statement 3** and **Statement 4**.