The relation connecting B, H nad I in SI system is

Options

A. B=H+1
B. B=H-1
C. `B=mu_(0)(H+1)`
D. `b=mu_(0)(H-I)`

Answer

To find the relation connecting B, H, and I in the SI system, we can start with Ampere's Circuital Law and the definitions of magnetic field strength and magnetic flux density.

### Step-by-Step Solution:

1. **Understanding the Terms**:
- \( B \) is the magnetic flux density (measured in teslas, T).
- \( H \) is the magnetic field intensity (measured in amperes per meter, A/m).
- \( I \) is the current flowing through a conductor (measured in amperes, A).

2. **Using Ampere's Circuital Law**:
- According to Ampere's Circuital Law, the relationship between \( B \) and \( H \) can be expressed as:
\[ B = \mu H \]
- Here, \( \mu \) is the permeability of the medium, which in free space is denoted as \( \mu_0 \) (the permeability of free space).

3. **Considering the Effect of Current**:
- When a current \( I \) flows through a conductor, it contributes to the magnetic field. The total magnetic field \( B \) can be expressed as:
\[ B = \mu_0 (H + I) \]
- This equation indicates that the magnetic flux density \( B \) is influenced by both the magnetic field intensity \( H \) and the current \( I \).

4. **Identifying the Correct Relation**:
- From the derived equation, we can see that the correct relation connecting \( B \), \( H \), and \( I \) in the SI system is:
\[ B = \mu_0 H + I \]
- This matches with option C from the given choices.

5. **Conclusion**:
- Thus, the correct relation connecting \( B \), \( H \), and \( I \) is:
\[ B = \mu_0 H + I \]

### Final Answer:
The relation connecting \( B \), \( H \), and \( I \) in the SI system is:
\[ B = \mu_0 H + I \]