A rectangular coil of 500 turn `10^(-2)m^(2)` area carrying 1 A is in a magnetic field of 1 T at 60° to its plane. The net rotating effect it could experience in (Nm) is

Options

A. 250
B. 25
C. 2.5
D. 0.25

Answer

To solve the problem of calculating the net rotating effect (torque) experienced by a rectangular coil in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of turns (N) = 500
- Area of the coil (A) = \(10^{-2} \, m^2\)
- Current (I) = 1 A
- Magnetic field (B) = 1 T
- Angle with respect to the plane of the coil = 60°

2. **Determine the angle between the magnetic field and the area vector:**
- The area vector is perpendicular to the plane of the coil. Since the magnetic field makes an angle of 60° with the plane, the angle (θ) between the magnetic field and the area vector is:
\[ \theta = 90° - 60° = 30° \]

3. **Use the formula for torque (τ):**
- The torque (τ) experienced by the coil in a magnetic field is given by the formula:
\[ τ = N \cdot I \cdot A \cdot B \cdot \sin(θ) \]

4. **Substitute the known values into the formula:**
- Plugging in the values:
\[ τ = 500 \cdot 1 \cdot 10^{-2} \cdot 1 \cdot \sin(30°) \]

5. **Calculate sin(30°):**
- We know that \(\sin(30°) = \frac{1}{2}\).

6. **Perform the calculation:**
- Substitute \(\sin(30°)\):
\[ τ = 500 \cdot 1 \cdot 10^{-2} \cdot 1 \cdot \frac{1}{2} \]
\[ τ = 500 \cdot 10^{-2} \cdot \frac{1}{2} = 500 \cdot 0.01 \cdot 0.5 \]
\[ τ = 5 \cdot 0.5 = 2.5 \, Nm \]

7. **Final Result:**
- The net rotating effect (torque) experienced by the coil is:
\[ τ = 2.5 \, Nm \]