A jet plane having a wing-span of 25 m is travelling horizontally towards East with a speed of 3600 km /hr. If the Earth's magnetic field at the location is `4 ×× 10 ^(-4)` T and the angle of dip is `30^@` , then the potential difference between the ends of the wing is

Options

A. (a)4 V
B. (b)5 V
C. (c)2 V
D. (d)2.5 V

Answer

To find the potential difference between the ends of the wings of a jet plane, we can follow these steps:

### Step 1: Understand the Problem
We have a jet plane with a wingspan of 25 m, traveling horizontally towards the east at a speed of 3600 km/h. The Earth's magnetic field at that location is \(4 \times 10^{-4}\) T, and the angle of dip is \(30^\circ\). We need to find the potential difference between the ends of the wings.

### Step 2: Convert Speed to m/s
First, we need to convert the speed from km/h to m/s:
\[ \text{Speed} = 3600 \, \text{km/h} = \frac{3600 \times 1000}{3600} \, \text{m/s} = 1000 \, \text{m/s} \]

### Step 3: Calculate the Vertical Component of the Magnetic Field
The vertical component of the Earth's magnetic field can be calculated using the formula:
\[ B_v = B \sin(\theta) \]
where \(B\) is the magnetic field strength and \(\theta\) is the angle of dip. Given \(B = 4 \times 10^{-4} \, \text{T}\) and \(\theta = 30^\circ\):
\[ B_v = 4 \times 10^{-4} \sin(30^\circ) \]
Since \(\sin(30^\circ) = \frac{1}{2}\):
\[ B_v = 4 \times 10^{-4} \times \frac{1}{2} = 2 \times 10^{-4} \, \text{T} \]

### Step 4: Calculate the Potential Difference
The potential difference (\(V\)) between the ends of the wings can be calculated using the formula:
\[ V = B_v \cdot v \cdot L \]
where \(v\) is the speed of the plane and \(L\) is the wingspan. Substituting the values:
\[ V = (2 \times 10^{-4} \, \text{T}) \cdot (1000 \, \text{m/s}) \cdot (25 \, \text{m}) \]
Calculating this gives:
\[ V = 2 \times 10^{-4} \cdot 1000 \cdot 25 = 2 \times 25 \times 10^{-1} = 50 \times 10^{-1} = 5 \, \text{V} \]

### Conclusion
The potential difference between the ends of the wings is \(5 \, \text{V}\).