Relation between `mu_(r)andchi` will be

Options

A. `mu_(r)=1+chi`
B. `chi=mu_(r)+1`
C. `mu_(0)/mu`
D. `mu_(0)chi`

Explanation

To find the relation between relative permeability (\( \mu_r \)) and magnetic susceptibility (\( \chi \)), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Relative permeability (\( \mu_r \)) is defined as the ratio of the permeability of a material (\( \mu \)) to the permeability of free space (\( \mu_0 \)):
\[ \mu_r = \frac{\mu}{\mu_0} \]
- Magnetic susceptibility (\( \chi \)) is a measure of how much a material will become magnetized in an applied magnetic field.

2. **Use the Relation of Permeability**:
- The permeability (\( \mu \)) of a material can be expressed in terms of the permeability of free space and the magnetic susceptibility:
\[ \mu = \mu_0 (1 + \chi) \]

3. **Substituting into the Relative Permeability Formula**:
- Substitute the expression for \( \mu \) into the relative permeability formula:
\[ \mu_r = \frac{\mu}{\mu_0} = \frac{\mu_0 (1 + \chi)}{\mu_0} \]

4. **Simplifying the Expression**:
- The \( \mu_0 \) terms cancel out:
\[ \mu_r = 1 + \chi \]

5. **Final Relation**:
- Thus, the relation between relative permeability and magnetic susceptibility is:
\[ \mu_r = 1 + \chi \]

### Conclusion:
The final relation between relative permeability (\( \mu_r \)) and magnetic susceptibility (\( \chi \)) is:
\[ \mu_r = 1 + \chi \]