The dimension of Curie constant is given by

Options

A. a.`M^(-1) L^(-1) T^(2) A^(2) K`
B. b.`K`
C. c.`M L T^(-2) A^(-2) K^(-1)`
D. d.`M T^(-2) A^(2) K`

Answer

To find the dimension of the Curie constant, we will follow these steps:

### Step 1: Understand the relationship between susceptibility and temperature
The susceptibility (χ) of a material is related to the Curie constant (C) and the temperature (T) by the equation:
\[ \chi = \frac{C}{T} \]

### Step 2: Rearranging the equation
From the above relationship, we can rearrange it to express the Curie constant:
\[ C = \chi \cdot T \]

### Step 3: Determine the dimensions of susceptibility
The susceptibility (χ) is defined as the relative permeability (μ_r) minus 1:
\[ \chi = \mu_r - 1 \]
Relative permeability (μ_r) is a dimensionless quantity, which means:
\[ \text{Dimension of } \chi = 1 \text{ (dimensionless)} \]

### Step 4: Determine the dimensions of temperature
The dimension of temperature (T) is represented as:
\[ \text{Dimension of } T = \Theta \]
where Θ is the dimension symbol for temperature.

### Step 5: Combine the dimensions
Now we can substitute the dimensions back into the equation for the Curie constant:
\[ \text{Dimension of } C = \text{Dimension of } \chi \cdot \text{Dimension of } T \]
Since the dimension of susceptibility is dimensionless:
\[ \text{Dimension of } C = 1 \cdot \Theta = \Theta \]

### Conclusion
Thus, the dimension of the Curie constant is:
\[ \text{Dimension of } C = \Theta \]