A train is moving towards north with a speed of 25 m/s. if the vertical component of the earth's magnetic field is `0.2 xx 10^(-4)` T, the emf induced in the axle 1.5 m long is

Options

A. 0.25 mV
B. 0.45 mV
C. 0.75 mV
D. 0.50 mV

Explanation

To find the induced electromotive force (emf) in the axle of the train, we can use the formula for motional emf:

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

where:
- \( E \) is the induced emf,
- \( B \) is the magnetic field strength (vertical component of the Earth's magnetic field),
- \( v \) is the velocity of the train,
- \( l \) is the length of the axle.

### Step 1: Identify the given values
- Speed of the train, \( v = 25 \, \text{m/s} \)
- Vertical component of the Earth's magnetic field, \( B = 0.2 \times 10^{-4} \, \text{T} \)
- Length of the axle, \( l = 1.5 \, \text{m} \)

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the formula:

\[ E = (0.2 \times 10^{-4} \, \text{T}) \cdot (25 \, \text{m/s}) \cdot (1.5 \, \text{m}) \]

### Step 3: Calculate the product
First, calculate \( 0.2 \times 25 \):

\[ 0.2 \times 25 = 5 \]

Next, multiply by \( 1.5 \):

\[ 5 \times 1.5 = 7.5 \]

Now, we include the \( 10^{-4} \):

\[ E = 7.5 \times 10^{-4} \, \text{V} \]

### Step 4: Convert to millivolts
To express the induced emf in millivolts, we convert volts to millivolts:

\[ E = 7.5 \times 10^{-4} \, \text{V} = 0.75 \, \text{mV} \]

### Final Answer
The induced emf in the axle is:

\[ E = 0.75 \, \text{mV} \]

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