The magnetic induction and magnetising field intensity in a sample of magnetic material are B and H respectively . The magnetic susceptibility of the material is

Options

A. `(B)/(mu_(0)H)`
B. `(B)/(mu_(0)H) -1`
C. `(B)/(H) -1`
D. `(mu_(0))H)/(B) -1`

Answer

To find the magnetic susceptibility (χ) of a magnetic material given the magnetic induction (B) and the magnetizing field intensity (H), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Magnetic induction (B) is the measure of the magnetic field produced in a material.
- Magnetizing field intensity (H) is the external magnetic field applied to the material.

2. **Relate Magnetic Induction and Magnetizing Field**:
- The relationship between magnetic induction (B) and magnetizing field intensity (H) is given by the equation:
\[ B = \mu H \]
where μ is the permeability of the material.

3. **Define Relative Permeability**:
- The relative permeability (μ_r) of a material is defined as:
\[ \mu_r = \frac{\mu}{\mu_0} \]
where μ_0 is the permeability of free space.

4. **Express Permeability in Terms of B and H**:
- From the equation \( B = \mu H \), we can express μ as:
\[ \mu = \frac{B}{H} \]

5. **Substitute into the Relative Permeability Equation**:
- Substitute μ into the relative permeability equation:
\[ \mu_r = \frac{B/H}{\mu_0} = \frac{B}{\mu_0 H} \]

6. **Relate Magnetic Susceptibility to Relative Permeability**:
- The magnetic susceptibility (χ) is related to relative permeability by:
\[ \chi = \mu_r - 1 \]
- Substituting the expression for μ_r:
\[ \chi = \frac{B}{\mu_0 H} - 1 \]

7. **Final Expression for Magnetic Susceptibility**:
- Rearranging gives us:
\[ \chi = \frac{B}{\mu_0 H} - 1 \]

### Conclusion:
The magnetic susceptibility (χ) of the material is given by:
\[ \chi = \frac{B}{\mu_0 H} - 1 \]