A magnet of magnetic moment `2*5Am^2` weighs `66g`. If density of material of the magnet is `7500 kg//m^3`, find the intensity of magnetisation.

Explanation

To find the intensity of magnetization (I) of the magnet, we will follow these steps:

### Step 1: Understand the formula for intensity of magnetization
The intensity of magnetization (I) is defined as the magnetic moment (M) per unit volume (V) of the magnet. The formula is given by:
\[ I = \frac{M}{V} \]

### Step 2: Identify the given values
From the problem, we have:
- Magnetic moment, \( M = 2.5 \, \text{Am}^2 \)
- Weight of the magnet, \( W = 66 \, \text{g} \)
- Density of the material, \( \rho = 7500 \, \text{kg/m}^3 \)

### Step 3: Convert the weight to mass
Since the weight is given in grams, we need to convert it to kilograms:
\[ \text{Mass} (m) = \frac{66 \, \text{g}}{1000} = 0.066 \, \text{kg} \]

### Step 4: Calculate the volume of the magnet
The volume (V) can be calculated using the formula:
\[ V = \frac{m}{\rho} \]
Substituting the values:
\[ V = \frac{0.066 \, \text{kg}}{7500 \, \text{kg/m}^3} \]
\[ V = \frac{0.066}{7500} \]
\[ V = 8.8 \times 10^{-6} \, \text{m}^3 \]

### Step 5: Calculate the intensity of magnetization
Now, we can find the intensity of magnetization using the formula:
\[ I = \frac{M}{V} \]
Substituting the values:
\[ I = \frac{2.5 \, \text{Am}^2}{8.8 \times 10^{-6} \, \text{m}^3} \]
\[ I = 2.84 \times 10^5 \, \text{A/m} \]

### Final Answer
Thus, the intensity of magnetization is:
\[ I \approx 2.84 \times 10^5 \, \text{A/m} \]

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