Electromagnetic Induction and aircraft wing

[Sabrina_18]

Homework Statement

4) The wing of an aircraft is 60m long and the aircraft is traveling at 250ms-1. The vertical component of the Earth’s magnetic field, which the wing is cutting, has the value of 4.3 X 10-5 T.
Calculate:
a. The Flux cut per second by the wing
b. The induced emf set up across the wing

Homework Equations

This s the equation given:
E = N D Φ /Dt

The Attempt at a Solution

Heres my attempt. My answers seem very wrong. Please help. Thanks.

a. The Flux cut per second by the wing
Magnetic field = 4.3 X 10-5 T
Length of conductor = 60m
Velocity = 250ms-1
E = Ф ÷ t
E = (4.3 X 10-5 X 60) ÷ 250 = 103 X 10-7 T

b. The induced emf set up across the wing
E = BLV
E = Induced EMF
B =Flux density
V = Velocity

E = 4.3 X 10-5 X 60 X 250 =0.645.

 

[alphysicist]

Hi Sabrina_18,

Homework Statement

4) The wing of an aircraft is 60m long and the aircraft is traveling at 250ms-1. The vertical component of the Earth’s magnetic field, which the wing is cutting, has the value of 4.3 X 10-5 T.
Calculate:
a. The Flux cut per second by the wing
b. The induced emf set up across the wing

Homework Equations

This s the equation given:
E = N D Φ /Dt

The Attempt at a Solution

Heres my attempt. My answers seem very wrong. Please help. Thanks.

a. The Flux cut per second by the wing
Magnetic field = 4.3 X 10-5 T
Length of conductor = 60m
Velocity = 250ms-1
E = Ф ÷ t
E = (4.3 X 10-5 X 60) ÷ 250 = 103 X 10-7 T

You're right that the thing you are looking for is flux/time. However, that will have units of T m^2 / s. What are the units of your calculation above (doing field times length over speed)? (You don't just get tesla.) Once you carry the units through your calculation, I think you'll see what you did wrong. What do you get?

 

[Moetasim]

I would first like to clarify that the given equation, E = NΦ/Δt, is for calculating the induced emf in a coil of wire due to a changing magnetic field, and may not be directly applicable to a wing of an aircraft cutting through the Earth's magnetic field. However, we can still use this equation to approximate the induced emf in the wing.

a. The Flux cut per second by the wing can be calculated by multiplying the magnetic field, length of the conductor (wing), and the velocity of the aircraft. This will give a value of 0.645 T-m/s or 6.45 X 10^-4 Wb/s.

b. To calculate the induced emf, we need to know the number of turns in the wing. Assuming there is only one turn, the induced emf can be calculated by multiplying the flux cut per second by the number of turns. This will give a value of 6.45 X 10^-4 V.

Please note that these calculations are based on approximations and may not accurately represent the actual values. Additionally, the induced emf in an aircraft wing may be affected by various factors such as the shape and material of the wing, and the orientation of the Earth's magnetic field. Further studies and experiments may be needed to accurately determine the induced emf in an aircraft wing.