In northern hemisphere, an airplane flies with a speed of `1000 km hr^(-1)` towards east at constant height. Calculate the emf induced between the tips of the wings 50 m apart. The vertical component of Earth's magnetic field is `2 xx 10^(-5) T`.

Answer

To solve the problem of calculating the induced EMF between the tips of the wings of an airplane flying in the northern hemisphere, we will follow these steps:

### Step 1: Understand the given data
- Speed of the airplane, \( V = 1000 \, \text{km/hr} \)
- Distance between the tips of the wings, \( L = 50 \, \text{m} \)
- Vertical component of Earth's magnetic field, \( B = 2 \times 10^{-5} \, \text{T} \)

### Step 2: Convert the speed from km/hr to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \, \text{km/hr} = \frac{1}{3.6} \, \text{m/s} \]
Thus,
\[ V = 1000 \, \text{km/hr} = 1000 \times \frac{1}{3.6} \, \text{m/s} \approx 277.78 \, \text{m/s} \]

### Step 3: Calculate the induced EMF using the formula
The formula for the induced EMF (\( \mathcal{E} \)) in a conductor moving in a magnetic field is given by:
\[ \mathcal{E} = B \cdot L \cdot V_{\perp} \]
Where:
- \( B \) is the magnetic field strength,
- \( L \) is the length of the conductor (distance between the tips of the wings),
- \( V_{\perp} \) is the component of the velocity perpendicular to the magnetic field.

In this case, since the airplane is flying east and the magnetic field has a vertical component, the entire speed of the airplane is perpendicular to the vertical magnetic field. Thus, we can take \( V_{\perp} = V \).

Substituting the values:
\[ \mathcal{E} = (2 \times 10^{-5} \, \text{T}) \cdot (50 \, \text{m}) \cdot (277.78 \, \text{m/s}) \]

### Step 4: Perform the calculation
Calculating the induced EMF:
\[ \mathcal{E} = 2 \times 10^{-5} \cdot 50 \cdot 277.78 \]
\[ \mathcal{E} = 2 \times 10^{-5} \cdot 13889 \]
\[ \mathcal{E} \approx 0.27778 \, \text{V} \]

### Step 5: Round the result
Rounding the result to two decimal places, we get:
\[ \mathcal{E} \approx 0.28 \, \text{V} \]

### Final Answer
The induced EMF between the tips of the wings is approximately \( 0.28 \, \text{V} \).

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