A straight conductor of length 4 m moves at a speed of 10 m/s when the conductor makes an angle of `30^(@)` with the direction of magnetic induction 0.1 T. then the induced emf is

Options

A. 1 V
B. 2 V
C. 4 V
D. 8 V

Explanation

To find the induced electromotive force (emf) in the given situation, we can use the formula for induced emf in a moving conductor within a magnetic field:

\[ \text{emf} = B \cdot v \cdot L \cdot \sin(\theta) \]

Where:
- \( B \) = magnetic field strength (in tesla)
- \( v \) = speed of the conductor (in m/s)
- \( L \) = length of the conductor (in meters)
- \( \theta \) = angle between the direction of motion and the magnetic field (in degrees)

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the conductor, \( L = 4 \, \text{m} \)
- Speed of the conductor, \( v = 10 \, \text{m/s} \)
- Magnetic field strength, \( B = 0.1 \, \text{T} \)
- Angle, \( \theta = 30^\circ \)

2. **Convert the angle to radians if necessary:**
- In this case, we can use \( \sin(30^\circ) \) directly, which is \( 0.5 \).

3. **Substitute the values into the formula:**
\[ \text{emf} = 0.1 \, \text{T} \cdot 10 \, \text{m/s} \cdot 4 \, \text{m} \cdot \sin(30^\circ) \]
\[ \text{emf} = 0.1 \cdot 10 \cdot 4 \cdot 0.5 \]

4. **Calculate the induced emf:**
\[ \text{emf} = 0.1 \cdot 10 \cdot 4 \cdot 0.5 = 0.1 \cdot 20 = 2 \, \text{V} \]

5. **Conclusion:**
The induced emf in the conductor is \( 2 \, \text{V} \).