When a piece of a ferromagnetic sobstance is put in a uniform magnetic field, the flux density inside it is four times the flux density away from the piece. The magnetic permeability of the material is

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To solve the problem, we need to determine the magnetic permeability of a ferromagnetic material when it is placed in a uniform magnetic field. The problem states that the flux density inside the material is four times the flux density outside of it.

### Step-by-Step Solution:

1. **Understanding Magnetic Flux Density**:
- Magnetic flux density (B) is defined as the amount of magnetic flux through a unit area. It is related to the magnetic field strength (H) and the magnetic permeability (μ) of the material by the equation:
\[ B = \mu H \]

2. **Setting Up the Problem**:
- Let \( B_0 \) be the magnetic flux density in the uniform magnetic field outside the ferromagnetic material.
- According to the problem, the flux density inside the material \( B \) is given by:
\[ B = 4B_0 \]

3. **Relating Magnetic Fields**:
- Using the relationship between magnetic flux density and magnetic field strength, we can express the magnetic flux densities:
\[ B_0 = \mu_0 H_0 \quad \text{(outside the material)} \]
\[ B = \mu H \quad \text{(inside the material)} \]
- Here, \( \mu_0 \) is the permeability of free space, and \( H_0 \) is the magnetic field strength outside the material.

4. **Substituting Values**:
- From the earlier equations, we can substitute \( B \) in terms of \( B_0 \):
\[ 4B_0 = \mu H \]
- Now, substituting \( B_0 \) in terms of \( H_0 \):
\[ 4(\mu_0 H_0) = \mu H \]

5. **Finding the Ratio of Magnetic Fields**:
- Rearranging the equation gives:
\[ \mu = \frac{4\mu_0 H_0}{H} \]
- Since the problem does not provide specific values for \( H_0 \) and \( H \), we can assume that the magnetic field strength inside the material \( H \) is related to the external field \( H_0 \) by the factor of permeability.

6. **Conclusion**:
- In a ferromagnetic material, the permeability \( \mu \) can be expressed as:
\[ \mu = 4\mu_0 \]
- Therefore, the magnetic permeability of the material is four times the permeability of free space.

### Final Answer:
The magnetic permeability of the material is \( \mu = 4\mu_0 \).

---