Which of the following statements are correct?

Options

A. Field inside an infinitely long solenoid is constant.
B. Field Inside a long cylindrical conductor carrying current parallel to its axis is `prop` r
C. Field Inside a long pipe carrying current parallel to its length is zero
D. Field outside a long current carrying wire is `prop (1//r^2)`

Answer

To solve the question regarding which statements about magnetic fields are correct, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A: The field inside an infinitely long solenoid is constant.**
- The magnetic field \( B \) inside an infinitely long solenoid is given by the formula:
\[ B = \mu_0 n I \]
where \( \mu_0 \) is the permeability of free space, \( n \) is the number of turns per unit length, and \( I \) is the current flowing through the solenoid. Since \( \mu_0 \), \( n \), and \( I \) are constants, the magnetic field inside the solenoid is indeed constant.
- **Conclusion:** Statement A is correct.

2. **Statement B: The field inside a long cylindrical conductor carrying current parallel to its axis is proportional to \( R \).**
- For a long cylindrical conductor, the magnetic field \( B \) at a distance \( R \) from the axis is given by:
\[ B = \frac{\mu_0 J R}{2} \]
where \( J \) is the current density. This shows that the magnetic field inside the conductor is directly proportional to the distance \( R \) from the axis.
- **Conclusion:** Statement B is correct.

3. **Statement C: The field inside a long pipe carrying current parallel to its length is 0.**
- For a long cylindrical pipe carrying current along its circumference, the current does not penetrate the interior of the pipe. According to Ampere's law, the magnetic field inside the hollow part of the pipe is:
\[ B = 0 \]
since there is no current enclosed by the Amperian loop inside the pipe.
- **Conclusion:** Statement C is correct.

4. **Statement D: The field outside a long current-carrying wire is proportional to \( \frac{1}{r^2} \).**
- The magnetic field \( B \) outside a long straight current-carrying wire at a distance \( r \) is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
This shows that the magnetic field is inversely proportional to \( r \), not \( \frac{1}{r^2} \).
- **Conclusion:** Statement D is incorrect.

### Final Summary:
The correct statements are A, B, and C.