Two rails of a railway track, insulated from each other and the ground, are connected to a millivoltmetre. What is the reading of the millivoltmetre when a train travels at a speed of 20 `ms^(-1)` along the track? Given that the vertical component of earth's magnetic field is `0.2xx10^(-4)"Wbm"^(-2)` and the rails are separated by 1 m

Options

A. 4 mV
B. 0.4 mV
C. 80 mV
D. 10 mV

Explanation

To solve the problem of finding the reading of the millivoltmetre when a train travels along the insulated railway track, we can use the concept of motional electromotive force (emf). The formula for the induced emf (ε) in a conductor moving through a magnetic field is given by:

\[ \epsilon = B \cdot l \cdot v \]

Where:
- \( \epsilon \) = induced emf (in volts)
- \( B \) = magnetic field strength (in Weber per square meter, Wb/m²)
- \( l \) = length of the conductor in the magnetic field (in meters)
- \( v \) = velocity of the conductor (in meters per second)

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Velocity of the train, \( v = 20 \, \text{m/s} \)
- Vertical component of Earth's magnetic field, \( B = 0.2 \times 10^{-4} \, \text{Wb/m}^2 \)
- Separation between the rails (length of the conductor), \( l = 1 \, \text{m} \)

2. **Substitute the Values into the Formula:**
\[ \epsilon = B \cdot l \cdot v \]
\[ \epsilon = (0.2 \times 10^{-4}) \cdot (1) \cdot (20) \]

3. **Calculate the Induced EMF:**
\[ \epsilon = 0.2 \times 10^{-4} \times 20 \]
\[ \epsilon = 4 \times 10^{-4} \, \text{V} \]

4. **Convert the Result to Millivolts:**
Since \( 1 \, \text{V} = 1000 \, \text{mV} \):
\[ \epsilon = 4 \times 10^{-4} \, \text{V} = 0.4 \, \text{mV} \]

5. **Final Reading on the Millivoltmetre:**
The reading of the millivoltmetre will be \( 0.4 \, \text{mV} \).

### Conclusion:
The reading of the millivoltmetre when the train is traveling at a speed of 20 m/s along the track is **0.4 mV**.

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