The relation between magnetic induction(B),magnetising field (H)And the magnetisation (I) is

Options

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

Answer

To find the relation between magnetic induction (B), magnetizing field (H), and magnetization (I), we can follow these steps:

### Step 1: Understand the Definitions
- **Magnetic Induction (B)**: This is the measure of the magnetic field created by the magnetization of a material.
- **Magnetizing Field (H)**: This is the external magnetic field applied to a material.
- **Magnetization (I)**: This is the magnetic moment per unit volume of the material.

### Step 2: Identify the Relationships
From the video transcript, we have the following relationships:
1. The magnetic susceptibility (χm) is defined as the ratio of magnetization (I) to the magnetizing field (H):
\[ \chi_m = \frac{I}{H} \]

2. The magnetic induction (B) is related to the magnetizing field (H) and the magnetization (I) through the equation:
\[ B = \mu_0 H + I \]
where \(\mu_0\) is the permeability of free space.

### Step 3: Substitute Magnetization in the Equation
We can express the magnetization (I) in terms of magnetic susceptibility (χm) and magnetizing field (H):
\[ I = \chi_m H \]

### Step 4: Substitute I in the B Equation
Now, substitute the expression for I into the equation for B:
\[ B = \mu_0 H + \chi_m H \]

### Step 5: Factor Out H
We can factor out H from the equation:
\[ B = H(\mu_0 + \chi_m) \]

### Step 6: Final Relation
Thus, the final relation between magnetic induction (B), magnetizing field (H), and magnetization (I) is:
\[ B = H(\mu_0 + \chi_m) \]

### Summary of the Relation
The relationship can be summarized as:
\[ B = \mu_0 H + I \]
or
\[ B = H(\mu_0 + \chi_m) \]