The magnetic moment associated with a circular coil of 35 turns and radius 25 cm, if it carries a current of 11 A is

Options

A. `72.2A m^(2)`
B. `70.5A m^(2)`
C. `74.56A m^(2)`
D. `75.56A m^(2)`

Explanation

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

\[ \mu = n \cdot I \cdot A \]

where:
- \(\mu\) is the magnetic moment,
- \(n\) is the number of turns in the coil,
- \(I\) is the current flowing through the coil, and
- \(A\) is the area of the coil.

### Step 1: Identify the given values
From the problem, we have:
- Number of turns, \(n = 35\)
- Radius of the coil, \(r = 25 \, \text{cm} = 25 \times 10^{-2} \, \text{m}\)
- Current, \(I = 11 \, \text{A}\)

### Step 2: Calculate the area of the coil
The area \(A\) of a circular coil is given by the formula:

\[ A = \pi r^2 \]

Substituting the value of \(r\):

\[ A = \pi (25 \times 10^{-2})^2 \]

Calculating \(r^2\):

\[ r^2 = (25 \times 10^{-2})^2 = 625 \times 10^{-4} = 6.25 \times 10^{-2} \, \text{m}^2 \]

Now substituting back to find \(A\):

\[ A = \pi \times 6.25 \times 10^{-2} \approx 3.14 \times 6.25 \times 10^{-2} \approx 0.19625 \, \text{m}^2 \]

### Step 3: Substitute values into the magnetic moment formula
Now we can substitute \(n\), \(I\), and \(A\) into the magnetic moment formula:

\[ \mu = n \cdot I \cdot A = 35 \cdot 11 \cdot 0.19625 \]

Calculating this step-by-step:

1. Calculate \(35 \cdot 11 = 385\).
2. Now multiply \(385 \cdot 0.19625 \approx 75.56 \, \text{A m}^2\).

### Final Answer
The magnetic moment associated with the circular coil is approximately:

\[ \mu \approx 75.56 \, \text{A m}^2 \]