An aeroplane is flying horizontally with a velocity of 360Km/hr. The distance between the tips of wings is 50m. If the vertical component of earth's magnetic field is `4xx10^(-4)T`, induced EMF across the wings is:

Options

A. 1 V
B. 100V
C. 1 kV
D. Zero

Answer

To solve the problem of finding the induced EMF across the wings of the airplane, we can follow these steps:

### Step 1: Convert the velocity from km/hr to m/s
The velocity of the airplane is given as 360 km/hr. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Velocity (m/s)} = \text{Velocity (km/hr)} \times \frac{5}{18} \]
Calculating:
\[ \text{Velocity} = 360 \times \frac{5}{18} = 100 \text{ m/s} \]

### Step 2: Identify the values needed for the induced EMF formula
We need the following values:
- Velocity (V) = 100 m/s (from Step 1)
- Vertical component of Earth's magnetic field (B) = \(4 \times 10^{-4} \text{ T}\)
- Distance between the tips of the wings (L) = 50 m

### Step 3: Use the formula for induced EMF
The induced EMF (ε) can be calculated using the formula:
\[ \text{Induced EMF} = V \times B \times L \]
Substituting the known values:
\[ \text{Induced EMF} = 100 \text{ m/s} \times 4 \times 10^{-4} \text{ T} \times 50 \text{ m} \]

### Step 4: Perform the calculation
Calculating the induced EMF:
\[ \text{Induced EMF} = 100 \times 4 \times 50 \times 10^{-4} \]
\[ = 20000 \times 10^{-4} = 2 \text{ V} \]

### Conclusion
The induced EMF across the wings of the airplane is **2 volts**.

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