A horizontal straight wire 20 m long extending from east to west falling with a speed of `5.0 m//s`, at right angles to the horizontal component of the earth’s magnetic field `0.30 × 10^(–4) Wb//m^(2)`. The instantaneous value of the e.m.f. induced in the wire will be

Options

A. `3 mV`
B. `4.5 mV`
C. `1.5 mV`
D. `6.0 mV`

Explanation

To find the instantaneous value of the electromotive force (e.m.f.) induced in the wire, we can use the formula for induced e.m.f. in a conductor moving through a magnetic field:

\[ \text{Induced EMF} (\epsilon) = B \cdot V \cdot L \]

Where:
- \( B \) is the magnetic field strength (in Weber per square meter, Wb/m²)
- \( V \) is the velocity of the wire (in meters per second, m/s)
- \( L \) is the length of the wire (in meters, m)

### Step-by-step Solution:

1. **Identify the given values:**
- Length of the wire, \( L = 20 \, \text{m} \)
- Velocity of the wire, \( V = 5.0 \, \text{m/s} \)
- Magnetic field strength, \( B = 0.30 \times 10^{-4} \, \text{Wb/m}^2 \)

2. **Substitute the values into the formula:**
\[ \epsilon = B \cdot V \cdot L \]
\[ \epsilon = (0.30 \times 10^{-4}) \cdot (5.0) \cdot (20) \]

3. **Calculate the product:**
- First, calculate \( 5.0 \cdot 20 = 100 \)
- Then, multiply by \( B \):
\[ \epsilon = 0.30 \times 10^{-4} \cdot 100 \]
\[ \epsilon = 30 \times 10^{-4} \, \text{V} \]

4. **Convert to millivolts:**
\[ \epsilon = 0.0030 \, \text{V} = 3.0 \, \text{mV} \]

5. **Final answer:**
The instantaneous value of the e.m.f. induced in the wire is \( 3.0 \, \text{mV} \).

### Conclusion:
The correct option for the induced e.m.f. is \( 3 \, \text{mV} \).