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A large jetliner with a wingspan of 40 m flies horizontally and due north at a speed of 300 m/s in a region where the magnetic field of earth is 60 uT directed 50 degrees below the horizontal. What is the magnitude of the induced emf between the ends of the wing?

a) 250 mV
b)350 mV
c) 550 mV
d) 750 mV

1 Answer

3 votes

Final answer:

Using Faraday's law of electromagnetic induction, the induced emf on a jetliner with a 40 m wingspan flying at 300 m/s through a 60 uT magnetic field directed 50 degrees below the horizontal is calculated to be 550 mV.

Step-by-step explanation:

The question involves calculating the induced electromotive force (emf) in the wings of a jetliner flying through the Earth's magnetic field, a concept from physics. By applying Faraday's law of electromagnetic induction, we can determine the induced emf when a conductor moves through a magnetic field.

To solve for the induced emf, we use the equation emf = B * v * l * sin(θ), where B is the magnetic field strength, v is the velocity of the conductor, l is the length of the conductor, and θ is the angle between the direction of velocity and the magnetic field. Since the magnetic field is directed 50 degrees below the horizontal and the plane is flying horizontally due north, the angle θ will be 90 degrees (because the movement is perpendicular to the direction of the magnetic field's horizontal component).

Thus, the induced emf is calculated as follows:

  • B = 60 uT = 60 x 10-6 T
  • v = 300 m/s
  • l = 40 m
  • sin(θ) = sin(90°) = 1

emf = 60 x 10-6 T * 300 m/s * 40 m * 1 = 0.72 V = 720 mV

However, since this value is not an option in the multiple-choice answers provided, we might consider only the vertical component of the magnetic field, which contributes to the induction effect:

  • Bvertical = B * sin(50°)
  • sin(50°) = 0.77 (approximately)
  • Bvertical = 60 x 10-6 T * 0.77 = 46.2 x 10-6 T
  • emf = 46.2 x 10-6 T * 300 m/s * 40 m * 1 = 0.55 V = 550 mV

Therefore, the correct answer is 550 mV, which corresponds to option (c).

User Magne Land
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