In the question number 73, for the coil given the magnetic moment is

Options

A. `12.95A m^(2)`
B. `25.79 A m^(2)`
C. `10.05 A m^(2)`
D. `24.79 A m^(2)`

Explanation

To find the magnetic moment of a circular coil, we can use the formula:

\[ \text{Magnetic Moment} (M) = n \cdot I \cdot A \]

Where:
- \( n \) = number of turns in the coil
- \( I \) = current flowing through the coil
- \( A \) = area of the coil

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of turns, \( n = 100 \)
- Current, \( I = 3.2 \, \text{A} \)
- Radius of the coil, \( R = 10 \, \text{cm} = 0.1 \, \text{m} \) (conversion from cm to m)

2. **Calculate the area of the circular coil:**
The area \( A \) of a circle is given by the formula:
\[ A = \pi R^2 \]
Substituting the value of \( R \):
\[ A = \pi (0.1)^2 = \pi \cdot 0.01 \, \text{m}^2 \]
Using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \cdot 0.01 = 0.0314 \, \text{m}^2 \]

3. **Substitute the values into the magnetic moment formula:**
\[ M = n \cdot I \cdot A \]
\[ M = 100 \cdot 3.2 \cdot 0.0314 \]

4. **Perform the multiplication:**
First, calculate \( 100 \cdot 3.2 = 320 \):
\[ M = 320 \cdot 0.0314 \]
Now, multiply:
\[ M \approx 10.048 \, \text{A m}^2 \]

5. **Round the result:**
Rounding to two decimal places, we get:
\[ M \approx 10.05 \, \text{A m}^2 \]

### Final Answer:
The magnetic moment of the coil is approximately \( 10.05 \, \text{A m}^2 \).