In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero.

Options

A. outside the cable
B. inside the inner conductor
C. inside the outer conductor
D. in between the two conductor

Answer

To solve the problem regarding the magnetic field in a coaxial cable with equal currents in opposite directions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have a coaxial cable consisting of a central conductor and an outer conductor. The central conductor carries a current \( I \) in one direction, while the outer conductor carries an equal current \( I \) in the opposite direction.

2. **Apply Ampere's Law**:
- According to Ampere's Law, the magnetic field \( B \) around a current-carrying conductor can be calculated using the formula:
\[ \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}} \]
- Here, \( I_{\text{enc}} \) is the current enclosed by the Amperian loop.

3. **Choose an Amperian Loop**:
- We can consider different Amperian loops: one inside the inner conductor, one in the space between the inner and outer conductors, and one outside the outer conductor.

4. **Evaluate the Magnetic Field in Different Regions**:
- **Inside the Inner Conductor**:
- The magnetic field \( B \) is zero because there is no current enclosed by the loop.
- **Between the Inner and Outer Conductor**:
- The enclosed current is \( I - I = 0 \) (since the currents are equal and opposite), thus:
\[ B = 0 \]
- **Outside the Outer Conductor**:
- The enclosed current is also zero because the currents cancel each other out, leading to:
\[ B = 0 \]

5. **Conclusion**:
- Since the magnetic field is zero in all regions (inside the inner conductor, between the conductors, and outside the outer conductor), we conclude that the magnetic field is indeed zero in the entire coaxial cable setup.

### Final Answer:
The magnetic field is zero in all regions: inside the inner conductor, between the two conductors, and outside the outer conductor.

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