A meter gauge train runs northwards with a constant speed of 22 m/s on a horizontal track. If the vertical component of the earth's magnetic field at that place is `3xx10^(-4)T`. The emf induced in its axle is

Options

A. 6.6 mV
B. 5.5 mV
C. 4.5 mV
D. 4.4 mV

Explanation

To solve the problem of finding the induced EMF in the axle of a meter gauge train moving northwards, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Speed of the train, \( V = 22 \, \text{m/s} \)
- Vertical component of the Earth's magnetic field, \( B = 3 \times 10^{-4} \, \text{T} \)
- Length of the axle (since it’s a meter gauge train), \( L = 1 \, \text{m} \)

2. **Understand the Configuration**:
- The train is moving northwards, and the vertical component of the magnetic field is directed downwards (into the plane).
- The velocity of the train, the length of the axle, and the magnetic field are mutually perpendicular.

3. **Use the Formula for Induced EMF**:
- The formula for the motional EMF induced in a conductor moving through a magnetic field is given by:
\[ \text{EMF} = V \times L \times B \]

4. **Substitute the Values**:
- Plugging in the values we have:
\[ \text{EMF} = 22 \, \text{m/s} \times 1 \, \text{m} \times 3 \times 10^{-4} \, \text{T} \]

5. **Calculate the EMF**:
- Performing the multiplication:
\[ \text{EMF} = 22 \times 1 \times 3 \times 10^{-4} = 66 \times 10^{-4} \, \text{V} \]
- Converting to millivolts:
\[ \text{EMF} = 6.6 \, \text{mV} \]

6. **Final Result**:
- The induced EMF in the axle of the train is \( 6.6 \, \text{mV} \).