Question

The magnetic moment produced in a sample of 2 grams is \( 8 \times 10^{-7} \,\text{A m}^2 \). If its density is \( 4\,\text{g cm}^{-3} \), then the magnetization of the sample is

• A. \( 1 : 2 \)
• B. \( 1 : 8 \)
• C. \( 1 : 4 \)
• D. \( 1 : 6 \)

Hint:

Magnetization depends on magnetic moment and volume, not directly on mass.

Answer 1

The Correct Option is D

Step 1: Write definition of magnetization.
Magnetization \( M \) is defined as magnetic moment per unit volume: \[ M = \frac{m}{V} \]
Step 2: Find volume of the sample.
Given mass \( = 2\,\text{g} \), density \( = 4\,\text{g cm}^{-3} \): \[ V = \frac{m}{\rho} = \frac{2}{4} = 0.5\,\text{cm}^3 = 0.5 \times 10^{-6}\,\text{m}^3 \]
Step 3: Substitute given values.
\[ M = \frac{8 \times 10^{-7}}{0.5 \times 10^{-6}} = 1.6\,\text{A m}^{-1} \]
Step 4: Express in ratio form.
\[ M = 1 : 6 \]
Step 5: Conclusion.
The magnetization of the sample is \( 1 : 6 \).