A 1.2 wide track is parallel to magnetic meridian . The verticle component of earth's magnetic field is 0.5 gauss. When a train runs on the rails at a speed of 60Km/hr, then the induced potential difference between the ends of its axle will be __

Options

A. `10^(-4)V`
B. `2xx10^(-4)V`
C. `10^(-3)V`
D. Zero

Answer

To solve the problem of finding the induced potential difference between the ends of the axle of a train running on rails in a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Width of the track (length of the axle, \( l \)) = 1.2 m
- Vertical component of Earth's magnetic field (\( B \)) = 0.5 Gauss
- Speed of the train (\( v \)) = 60 km/hr

2. **Convert the Magnetic Field from Gauss to Tesla:**
- We know that \( 1 \text{ Gauss} = 10^{-4} \text{ Tesla} \).
- Therefore, \( B = 0.5 \text{ Gauss} = 0.5 \times 10^{-4} \text{ Tesla} = 5 \times 10^{-5} \text{ Tesla} \).

3. **Convert the Speed from km/hr to m/s:**
- To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
- Thus, \( v = 60 \text{ km/hr} \times \frac{5}{18} = \frac{300}{18} \text{ m/s} = 16.67 \text{ m/s} \).

4. **Use the Formula for Induced EMF:**
- The induced EMF (\( \epsilon \)) can be calculated using the formula:
\[ \epsilon = B \cdot l \cdot v \]
- Here, \( B \) is the magnetic field in Tesla, \( l \) is the length of the track in meters, and \( v \) is the speed in m/s.

5. **Substitute the Values:**
- Plugging in the values:
\[ \epsilon = (5 \times 10^{-5} \text{ T}) \cdot (1.2 \text{ m}) \cdot (16.67 \text{ m/s}) \]

6. **Calculate the Induced EMF:**
- Performing the multiplication:
\[ \epsilon = 5 \times 10^{-5} \cdot 1.2 \cdot 16.67 \]
- First calculate \( 1.2 \cdot 16.67 \):
\[ 1.2 \cdot 16.67 \approx 20.004 \text{ (approximately 20)} \]
- Now, calculate:
\[ \epsilon \approx 5 \times 10^{-5} \cdot 20 = 1 \times 10^{-4} \text{ V} \]

7. **Final Result:**
- The induced potential difference between the ends of the axle is approximately:
\[ \epsilon = 0.0001 \text{ V} = 10^{-4} \text{ V} \]

### Conclusion:
The induced potential difference between the ends of the axle of the train is \( 10^{-4} \) V.

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