2 m long wire moving with `v = 1 ms^(-1)` in magnetic field intensity `0.5 Wb m^(-2)` perpendicular to the field. The induced emf is':

Options

A. 0.1 V
B. 0.2 V
C. 0.5 V
D. 1 V

Explanation

To solve the problem of finding the induced EMF in a wire moving in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Length of the wire (L) = 2 m
- Velocity of the wire (v) = 1 m/s
- Magnetic field intensity (B) = 0.5 Wb/m² (Tesla)

2. **Understand the Formula for Induced EMF**:
The formula to calculate the induced EMF (E) when a wire moves in a magnetic field is given by:
\[ E = B \cdot L \cdot v \]
where:
- E is the induced EMF,
- B is the magnetic field strength,
- L is the length of the wire,
- v is the velocity of the wire.

3. **Substitute the Values into the Formula**:
Now, we can substitute the values we have into the formula:
\[ E = 0.5 \, \text{Wb/m}^2 \cdot 2 \, \text{m} \cdot 1 \, \text{m/s} \]

4. **Calculate the Induced EMF**:
Performing the multiplication:
\[ E = 0.5 \cdot 2 \cdot 1 = 1 \, \text{V} \]

5. **Conclusion**:
The induced EMF in the wire is 1 V.