A Boeing 747 jet with a wingspan of 60.0 m is flying horizontally at a speed of 287 m/s over Phoenix, Arizona, at a location where the Earth's magnetic field is 50.2 µT at 58.0° below the horizontal. What voltage is generated between the wingtips?
wouldln't it be Voltage=Bperpendicular*velcoity*wingspan?
check my thinking.
To determine the voltage generated between the wingtips of the Boeing 747 jet, we can use the equation:
V = B * L * v * sin(theta),
where:
V is the voltage,
B is the magnetic field strength,
L is the length of the wing (wingspan),
v is the velocity of the aircraft, and
theta is the angle between the wingspan and the horizontal direction.
Given:
B = 50.2 µT = 50.2 * 10^-6 T (tesla)
L = wingspan = 60.0 m
v = velocity = 287 m/s
theta = 58.0°
Converting the angle to radians:
theta = 58.0° * (π/180) = 1.0122922 radians
Now we can substitute these values into the equation:
V = (50.2 * 10^-6 T) * (60.0 m) * (287 m/s) * sin(1.0122922)
Calculating the value:
V = (50.2 * 10^-6) * (60.0) * (287) * sin(1.0122922)
V ≈ 4.83 volts
Therefore, the voltage generated between the wingtips of the Boeing 747 jet is approximately 4.83 volts.
To calculate the voltage generated between the wingtips of the Boeing 747 jet, you need to use the formula for the electromotive force (EMF) induced in a conductor moving perpendicularly in a magnetic field. The formula is given by:
EMF = B * L * v * sin(θ)
Where:
B is the magnetic field strength
L is the length of the conductor perpendicular to the magnetic field
v is the velocity of the conductor
θ is the angle between the velocity vector and the magnetic field vector
In this case, the wing of the Boeing 747 jet can be considered as the conductor moving through the Earth's magnetic field. The wingspan (60.0 m) represents the length of the conductor perpendicular to the magnetic field.
Now, let's break down the given information and solve for the voltage:
1. Magnetic Field Strength (B): The Earth's magnetic field is given as 50.2 µT. However, we need to convert it to Tesla (T) to maintain units consistency. 1 µT = 1 x 10^-6 T. Therefore, B = 50.2 x 10^-6 T.
2. Length of Conductor (L): The length of the conductor is the wingspan of the Boeing 747 jet, which is given as 60.0 m.
3. Velocity of Conductor (v): The Boeing 747 jet is flying at a speed of 287 m/s horizontally.
4. Angle (θ): The angle is given as 58.0° below the horizontal. Since the velocity vector is horizontal, the angle between the velocity vector and the magnetic field vector is 90° - 58.0° = 32.0°.
Now we can plug in these values into the formula and calculate the EMF:
EMF = (50.2 x 10^-6 T) * (60.0 m) * (287 m/s) * sin(32.0°)
Calculating this expression will give us the voltage generated between the wingtips of the jet.