Which of the following relations is not correct?

Options

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

Answer

To determine which of the given relations is not correct, we will analyze each option step by step.

### Step 1: Analyze the First Option
The first option relates the magnetic field \( B \) and the magnetic field strength \( H \). The relation is given by:
\[ H = \frac{B}{\mu} \]
where \( \mu \) is the permeability of the medium. In a vacuum, this can be expressed as:
\[ B = \mu_0 H \]
This relation is correct as it follows from the definitions of \( B \) and \( H \).

**Hint:** Check the definitions of magnetic field \( B \) and magnetic field strength \( H \) to confirm their relationship.

### Step 2: Analyze the Second Option
The second option involves the magnetic field due to a solenoid. The magnetic field \( B \) in a solenoid is given by:
\[ B = \mu n I \]
where \( \mu \) is the permeability, \( n \) is the turns density, and \( I \) is the current. The permeability can be expressed as:
\[ \mu = \mu_0 (1 + \chi) \]
where \( \chi \) is the magnetic susceptibility. Thus, we can rewrite the magnetic field as:
\[ B = \mu_0 n I (1 + \chi) \]
This relation is also correct.

**Hint:** Recall the formula for the magnetic field in a solenoid and how permeability relates to susceptibility.

### Step 3: Analyze the Third Option
The third option discusses the direction of the magnetic field. The relation can change based on the orientation of the magnetic field lines, which can be represented with a plus or minus sign depending on the direction. This means the relation can be valid in both configurations.

**Hint:** Consider how the direction of magnetic fields can affect their representation in equations.

### Step 4: Analyze the Fourth Option
The fourth option states:
\[ \mu = 1 + \chi \]
This is incorrect. The correct relation is:
\[ \mu = \mu_0 (1 + \chi) \]
This means that the fourth option does not correctly represent the relationship between permeability and magnetic susceptibility.

**Hint:** Verify the correct formula relating permeability and susceptibility, paying attention to the constant \( \mu_0 \).

### Conclusion
After analyzing all four options, we find that the fourth option is the incorrect relation. Therefore, the answer to the question is:

**Answer:** Option 4 is not a correct relation.