A jet aircraft is flying due south at 300 m/s at a place where the earth’s magnetic field is 80 µT. Find the potential difference between the wing tips if they are 25 m apart. Which tip has the higher potential?
E=BxV where the important part of B is that which is perpendicular to v.
In general, the solution would be
emf=80E-6T*25m*300m/s*sinTheta, where theta is the angle below the horizon (assuming the plane is flying level). If in this case, the plane is flying due south say at the equator, and the magnetic field at the equator is parallel with the planes path, zero potential. So, more information on the inclination of the Magnetic field is needed.
To find the potential difference between the wing tips and determine which tip has the higher potential, we can use the formula:
V = B * v * d
where:
V is the potential difference in volts (V)
B is the magnetic field strength in Teslas (T)
v is the velocity of the aircraft perpendicular to the magnetic field in meters per second (m/s)
d is the distance between the wing tips in meters (m)
Given:
B = 80 µT = 80 * 10^(-6) T
v = 300 m/s
d = 25 m
Calculating the potential difference (V):
V = (80 * 10^(-6)) * 300 * 25
V = 0.06 V
The potential difference between the wing tips is 0.06 volts.
To determine which tip has the higher potential, we need to know the direction of the magnetic field relative to the aircraft's motion. The potential difference will depend on whether the wing tip moving towards the north or south pole of the magnetic field.
If the wing tip moving towards the south pole, it will have a higher potential. If the wing tip moving towards the north pole, it will have a lower potential.
To find the potential difference between the wing tips of the aircraft, we need to calculate the induced voltage due to the motion of the aircraft in the Earth's magnetic field. Here are the steps to find the answer:
1. Determine the formula for calculating the induced voltage. The formula is given by:
Induced Voltage (V) = B * L * V,
where B is the magnetic field strength, L is the length of the wing tips, and V is the velocity of the aircraft.
2. Convert the magnetic field strength from microteslas (µT) to teslas (T). Since 1 T = 1,000,000 µT, the conversion will be:
B = 80 µT / 1,000,000 = 0.000080 T.
3. Substitute the given values into the formula. The length of the wing tips, L, is given as 25 m, and the velocity, V, is given as 300 m/s:
V = (0.000080 T) * (25 m) * (300 m/s).
4. Calculate the induced voltage:
V = 0.000080 T * 25 m * 300 m/s = 0.000600 V.
Therefore, the potential difference between the wing tips of the aircraft is 0.000600 V.
As for which tip has the higher potential, it depends on the direction of the induced voltage. Since the aircraft is flying due south, the tip of the aircraft flying towards the south will be at a higher potential, while the tip flying towards the north will be at a lower potential.