An aircraft has a wing span of 56 m. It is flying horizontally at a speed of 900 km/hr and the vertical component of earth’s magnetic field is 0.4 m Wb/m2. Calculate the P.D between the wing tips of the air craft
To calculate the potential difference (P.D) between the wing tips of the aircraft, we can use the formula:
P.D = B × v × L
where:
- P.D is the potential difference,
- B is the magnetic field strength (vertical component of Earth's magnetic field),
- v is the velocity of the aircraft,
- L is the wing span of the aircraft.
Given:
- Wing span of the aircraft (L) = 56 m
- Velocity (v) = 900 km/hr = 900,000 m/hr = 900,000/3600 m/s = 250 m/s
- Magnetic field strength (B) = 0.4 m Wb/m²
Substituting these values into the formula:
P.D = (0.4 m Wb/m²) × (250 m/s) × (56 m)
P.D = 0.4 × 250 × 56 m² Wb
P.D = 5600 m² Wb
Therefore, the potential difference between the wing tips of the aircraft is 5600 m² Wb.
To calculate the potential difference (P.D) between the wing tips of the aircraft, we need to apply the formula for electromagnetic induction. According to Faraday's law of electromagnetic induction, the induced voltage (P.D) can be calculated by multiplying the rate of change of the magnetic field with respect to time (dB/dt) and the length of the conductor (wing span).
Here are the steps to calculate the P.D between the wing tips:
Step 1: Convert the given wing span from meters to kilometers.
- Wing span = 56 meters
- Wing span in kilometers = 56/1000 = 0.056 km
Step 2: Convert the given speed of the aircraft from kilometers per hour to meters per second.
- Speed of aircraft = 900 km/hr
- Speed of aircraft in m/s = (900 x 1000) / (60 x 60) = 250 m/s
Step 3: Calculate the rate of change of the magnetic field.
- Rate of change of magnetic field (dB/dt) = vertical component of the earth's magnetic field
- Given: dB/dt = 0.4 m Wb/m2
Step 4: Calculate the potential difference (P.D) between the wing tips.
- P.D = (dB/dt) x (wing span) x (velocity)
- P.D = 0.4 x 0.056 x 250
- P.D = 5.6 volts
Therefore, the potential difference (P.D) between the wing tips of the aircraft is 5.6 volts.