A circular coil of 50 turns and radius 20 cm carries a current of 12A. Find magnetic moment associated with it

Options

A. 72.5 `Am^(2)`
B. `75.4 Am^(2)`
C. `76.7 mA^(2)`
D. `70 Am^(2)`

Explanation

To find the magnetic moment associated with a circular coil, we can follow these steps:

### Step 1: Identify the given values
- Number of turns (N) = 50
- Radius of the coil (r) = 20 cm = 0.2 m (convert cm to m)
- Current (I) = 12 A

### Step 2: Calculate the area (A) of the circular coil
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (0.2)^2 = \pi (0.04) = 0.04\pi \, \text{m}^2 \]

### Step 3: Use the formula for magnetic moment (μ)
The magnetic moment \( \mu \) of a coil is given by the formula:
\[ \mu = N \times I \times A \]
Substituting the values we have:
\[ \mu = 50 \times 12 \times (0.04\pi) \]

### Step 4: Calculate the magnetic moment
First, calculate \( 50 \times 12 \):
\[ 50 \times 12 = 600 \]
Now, substituting this into the equation:
\[ \mu = 600 \times (0.04\pi) \]
Calculating \( 0.04\pi \):
\[ 0.04\pi \approx 0.1256 \, \text{m}^2 \]
Now, multiply:
\[ \mu = 600 \times 0.1256 \approx 75.36 \, \text{A m}^2 \]

### Step 5: Round the answer
Rounding to one decimal place, we get:
\[ \mu \approx 75.4 \, \text{A m}^2 \]

### Final Answer
The magnetic moment associated with the coil is approximately \( 75.4 \, \text{A m}^2 \).

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