Magnetic susceptibility of diamagnetic substances depends upon the absolute temperature T as

Options

A. `T^(1)`
B. `T^(-1)`
C. `T^(-2)`
D. `T^(0)`

Answer

To solve the question regarding the dependence of magnetic susceptibility of diamagnetic substances on absolute temperature \( T \), we can follow these steps:

### Step 1: Understand Magnetic Susceptibility
Magnetic susceptibility (\( \chi_m \)) is a measure of how much a material will become magnetized in an applied magnetic field. For diamagnetic materials, this value is negative.

### Step 2: Identify the Relative Permeability
The relative permeability (\( \mu_r \)) of a material is defined as the ratio of the permeability of the material to the permeability of free space. For diamagnetic materials, it is known that:
\[ \mu_r < 1 \]
In some cases, it can be approximated as:
\[ \mu_r \approx 0 \]

### Step 3: Relate Magnetic Susceptibility and Relative Permeability
There is a direct relationship between magnetic susceptibility and relative permeability given by the formula:
\[ \chi_m = \mu_r - 1 \]
Since \( \mu_r < 1 \), we can conclude:
\[ \chi_m < 0 \]

### Step 4: Analyze Temperature Dependence
For diamagnetic materials, it is established that the magnetic susceptibility is independent of temperature. This means that as the temperature changes, the magnetic susceptibility remains constant.

### Step 5: Conclusion
Thus, we can conclude that the magnetic susceptibility of diamagnetic substances does not depend on the absolute temperature \( T \).

### Final Answer
The magnetic susceptibility of diamagnetic substances is independent of the absolute temperature \( T \).

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