The wing span of an aeroplane is `20` metre. It is flying in a field, where the verticle component of magnetic field of earth is `5xx10^(-5)` tesla, with velocity `360 km//h`. The potential difference produced between the blades will be

Options

A. `0.10`V
B. `0.15`V
C. `0.20`V
D. `0.30`V

Answer

To solve the problem, we will calculate the potential difference (induced EMF) produced between the blades of the airplane using the formula for electromagnetic induction. Here’s the step-by-step solution:

### Step 1: Identify the given data
- Wing span (L) = 20 meters
- Vertical component of magnetic field (B) = \(5 \times 10^{-5}\) Tesla
- Velocity (V) = 360 km/h

### Step 2: Convert the velocity from km/h to m/s
To convert kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} \]
Thus,
\[ V = 360 \text{ km/h} = 360 \div 3.6 = 100 \text{ m/s} \]

### Step 3: Use the formula for induced EMF
The induced EMF (E) can be calculated using the formula:
\[ E = B \times L \times V \]
Where:
- \(E\) = induced EMF (in volts)
- \(B\) = magnetic field (in Tesla)
- \(L\) = length (in meters)
- \(V\) = velocity (in meters per second)

### Step 4: Substitute the values into the formula
Now substituting the values we have:
\[ E = (5 \times 10^{-5} \text{ T}) \times (20 \text{ m}) \times (100 \text{ m/s}) \]

### Step 5: Calculate the induced EMF
Calculating the expression:
\[ E = 5 \times 10^{-5} \times 20 \times 100 \]
\[ E = 5 \times 20 \times 100 \times 10^{-5} \]
\[ E = 1000 \times 10^{-5} = 0.10 \text{ volts} \]

### Conclusion
The potential difference produced between the blades of the airplane is \(0.10\) volts.

---