A circular coil of 25 turns and radius 12 cm is placed in a uniform magnetic field of 0.5 T normal to the plane of the coil. If the current in the coil is 6 A then total torque acting on the coil is

Options

A. zero
B. 3.4 Nm
C. 3.8 Nm
D. 4.4 Nm

Explanation

To solve the problem of finding the total torque acting on a circular coil placed in a magnetic field, we can follow these steps:

### Step 1: Understand the given data
- Number of turns (N) = 25
- Radius of the coil (r) = 12 cm = 0.12 m (convert to meters)
- Magnetic field strength (B) = 0.5 T
- Current in the coil (I) = 6 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 radius:
\[ A = \pi (0.12)^2 \]
\[ A = \pi (0.0144) \]
\[ A \approx 0.04524 \, \text{m}^2 \]

### Step 3: Calculate the magnetic moment (m) of the coil
The magnetic moment (m) of the coil can be calculated using the formula:
\[ m = N \cdot I \cdot A \]
Substituting the values:
\[ m = 25 \cdot 6 \cdot 0.04524 \]
\[ m = 25 \cdot 0.27144 \]
\[ m \approx 6.786 \, \text{A m}^2 \]

### Step 4: Calculate the torque (τ) acting on the coil
The torque (τ) acting on the coil in a magnetic field is given by:
\[ \tau = m \cdot B \cdot \sin(\theta) \]
Since the magnetic field is normal to the plane of the coil, the angle θ = 90 degrees, and sin(90°) = 1. Thus:
\[ \tau = m \cdot B \]
Substituting the values:
\[ \tau = 6.786 \cdot 0.5 \]
\[ \tau \approx 3.393 \, \text{Nm} \]

### Final Answer
The total torque acting on the coil is approximately **3.393 Nm**.

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