At a temperature of `30^(@)C`, the susceptibility of ferromagnetic material is found to be `'chi'` its susceptibility at `333^(@)C` is

Options

A. 0.5 X
B. 2 X
C. 11.1 X
D. 0.09 X

Answer

To solve the problem of finding the susceptibility of a ferromagnetic material at a temperature of 333°C given its susceptibility at 30°C, we can use Curie's Law.

### Step-by-Step Solution:

1. **Understanding Curie's Law**:
Curie's Law states that the magnetic susceptibility (χ) of a ferromagnetic material is inversely proportional to its absolute temperature (T). Mathematically, this can be expressed as:
\[ \chi \propto \frac{1}{T} \]
or
\[ \chi = \frac{C}{T} \]
where C is a constant (Curie's constant).

2. **Setting Up the Equation**:
From the above relationship, we can set up the following ratio for two different temperatures:
\[ \frac{\chi_1}{\chi_2} = \frac{T_2}{T_1} \]
where:
- \(\chi_1\) = susceptibility at \(T_1 = 30°C\)
- \(\chi_2\) = susceptibility at \(T_2 = 333°C\)

3. **Converting Temperatures to Kelvin**:
We need to convert the temperatures from Celsius to Kelvin:
- \(T_1 = 30 + 273 = 303 K\)
- \(T_2 = 333 + 273 = 606 K\)

4. **Substituting Values into the Ratio**:
Now we substitute the values into the ratio:
\[ \frac{\chi}{\chi_2} = \frac{606}{303} \]

5. **Calculating the Ratio**:
Simplifying the right side:
\[ \frac{606}{303} = 2 \]
Therefore, we can express this as:
\[ \chi = 2 \chi_2 \]

6. **Finding \(\chi_2\)**:
Rearranging the equation gives:
\[ \chi_2 = \frac{\chi}{2} \]
Thus, if \(\chi\) is the susceptibility at 30°C, then at 333°C, the susceptibility will be:
\[ \chi_2 = 0.5 \chi \]

### Final Answer:
The susceptibility of the ferromagnetic material at 333°C is \(0.5 \chi\).