If a long hollow copper pipe carriers a direct current, the magnetic field associated with the current will be:

Options

A. inside the pipe only
B. outside the pipe only
C. both inside and outside the pipe
D. no where

Answer

To solve the problem, we need to determine the magnetic field associated with a long hollow copper pipe carrying a direct current. We will analyze the situation using Ampere's Circuital Law.

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have a long hollow copper pipe through which a direct current (I) is flowing. The current can be assumed to flow uniformly along the length of the pipe.

2. **Identify Regions**:
- There are two regions to consider:
- Inside the hollow pipe
- Outside the hollow pipe

3. **Apply Ampere's Circuital Law**:
- According to Ampere's Circuital Law, the line integral of the magnetic field (B) around a closed loop is equal to the permeability of free space (μ₀) times the current enclosed (I_enclosed) by that loop.
- Mathematically, it is expressed as:
\[ \oint B \cdot dl = \mu_0 I_{\text{enclosed}} \]

4. **Analyze the Inside of the Pipe**:
- If we consider a circular loop inside the hollow part of the pipe, there is no current enclosed by this loop because the current flows along the surface of the pipe.
- Therefore, applying Ampere's Law:
\[ I_{\text{enclosed}} = 0 \implies B_{\text{inside}} = 0 \]

5. **Analyze the Outside of the Pipe**:
- Now consider a circular loop outside the hollow pipe. In this case, the entire current (I) flowing through the pipe is enclosed by the loop.
- Thus, applying Ampere's Law:
\[ I_{\text{enclosed}} = I \implies B_{\text{outside}} = \frac{\mu_0 I}{2 \pi r} \]
- Here, r is the distance from the center of the pipe to the point where we are calculating the magnetic field.

6. **Conclusion**:
- From the analysis, we conclude that:
- The magnetic field inside the hollow copper pipe is zero (B_inside = 0).
- The magnetic field outside the hollow copper pipe is non-zero and can be calculated using the formula derived above (B_outside ≠ 0).

### Final Answer:
The magnetic field associated with the current will be **zero inside the pipe** and **non-zero outside the pipe**.