A solid metallic cylinder carriers a direct current. The magnetic field produce by it exists

Options

A. Outside only
B. Inside only
C. Both inside and outside
D. neither inside nor outside

Answer

To solve the question regarding the magnetic field produced by a solid metallic cylinder carrying a direct current, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine where the magnetic field exists when a solid metallic cylinder carries a direct current. The options are: outside only, inside only, both inside and outside, or neither inside nor outside.

**Hint**: Consider the properties of magnetic fields generated by current-carrying conductors.

2. **Visualizing the Cylinder**:
Imagine a solid metallic cylinder. The current flows uniformly throughout the volume of the cylinder since it is solid.

**Hint**: Draw a diagram of the cylinder and indicate the direction of current flow.

3. **Applying 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 \( \mu_0 \) (the permeability of free space) times the current enclosed by that loop:
\[ \oint B \cdot dl = \mu_0 I_{\text{enclosed}} \]

**Hint**: Remember that the current enclosed will affect the magnetic field both inside and outside the cylinder.

4. **Analyzing Inside the Cylinder**:
If we draw a loop inside the solid cylinder, the current enclosed by this loop is not zero because the current flows through the entire volume of the cylinder. Therefore, there will be a magnetic field inside the cylinder.

**Hint**: Consider how the current distribution affects the magnetic field inside the cylinder.

5. **Analyzing Outside the Cylinder**:
When we consider a loop outside the cylinder, the total current flowing through the cylinder contributes to the magnetic field outside as well. Hence, the magnetic field exists outside the cylinder too.

**Hint**: Think about how the magnetic field behaves in relation to the total current flowing through the cylinder.

6. **Conclusion**:
Since the magnetic field exists both inside and outside the solid metallic cylinder due to the presence of current throughout its volume, the correct answer is that the magnetic field exists in both regions.

**Hint**: Summarize your findings to confirm the presence of the magnetic field in both locations.

### Final Answer:
The magnetic field produced by a solid metallic cylinder carrying a direct current exists both inside and outside the cylinder.