A current of `5A` is flowing through a 10 turn circular coil of radius `7cm`. The coil lies in XY plane. What is the magnitude and direction of magnetic dipole moment associated with it?

Explanation

To find the magnitude and direction of the magnetic dipole moment associated with a circular coil carrying a current, we can follow these steps:

### Step 1: Identify the given values
- Current (I) = 5 A
- Number of turns (n) = 10
- Radius of the coil (r) = 7 cm = 0.07 m (convert cm to m)

### Step 2: Calculate the area of the coil
The area (A) of a circular coil can be calculated using the formula:
\[ A = \pi r^2 \]
Substituting the value of r:
\[ A = \pi (0.07)^2 \]
\[ A = \pi (0.0049) \]
\[ A \approx 0.0154 \, \text{m}^2 \]

### Step 3: Calculate the magnetic dipole moment (M)
The magnetic dipole moment (M) is given by the formula:
\[ M = n \times I \times A \]
Substituting the known values:
\[ M = 10 \times 5 \times 0.0154 \]
\[ M = 10 \times 5 \times 0.0154 \]
\[ M = 0.77 \, \text{A m}^2 \]

### Step 4: Determine the direction of the magnetic dipole moment
The direction of the magnetic dipole moment is given by the right-hand rule. Since the coil lies in the XY plane, the magnetic dipole moment will be directed perpendicular to this plane, which is along the Z-axis.

### Final Answer:
- **Magnitude of the magnetic dipole moment (M)**: 0.77 A m²
- **Direction**: Perpendicular to the plane of the coil (along the Z-axis)

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