A circular coil of 25 turns and radius of 12 cm is placed in a uniform magnetic field of 0.5 T normal to the plane of coil. If the current in the coil is 5 A, then total torque experienced by the coil is

Options

A. 1.5Nm
B. 2.5Nm
C. 3.5Nm
D. zero

Explanation

To find the total torque experienced by a circular coil placed in a magnetic field, we can follow these steps:

### Step 1: Understand the Formula for Torque
The torque (\( \tau \)) experienced by a coil in a magnetic field is given by the formula:
\[ \tau = m \cdot B \cdot \sin(\theta) \]
where:
- \( m \) is the magnetic moment,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the magnetic moment and the magnetic field.

### Step 2: Identify the Given Values
From the problem, we have:
- Number of turns in the coil (\( n \)) = 25
- Radius of the coil (\( r \)) = 12 cm = 0.12 m
- Magnetic field (\( B \)) = 0.5 T
- Current (\( I \)) = 5 A

### Step 3: Calculate the Area of the Coil
The area (\( A \)) of the circular coil is given by:
\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (0.12)^2 = \pi (0.0144) \approx 0.04524 \, \text{m}^2 \]

### Step 4: Calculate the Magnetic Moment
The magnetic moment (\( m \)) is given by:
\[ m = n \cdot I \cdot A \]
Substituting the known values:
\[ m = 25 \cdot 5 \cdot 0.04524 \approx 5.653 \, \text{A m}^2 \]

### Step 5: Determine the Angle
Since the magnetic field is normal to the plane of the coil, the angle \( \theta \) is 90 degrees. Thus, \( \sin(90^\circ) = 1 \).

### Step 6: Calculate the Torque
Now substituting \( m \), \( B \), and \( \sin(\theta) \) into the torque formula:
\[ \tau = m \cdot B \cdot \sin(90^\circ) = m \cdot B \]
\[ \tau = 5.653 \cdot 0.5 = 2.8265 \, \text{N m} \]

### Step 7: Final Answer
The total torque experienced by the coil is approximately:
\[ \tau \approx 2.83 \, \text{N m} \]