An horizontally flying airplane has a 20 m wing span. If the vertical component of the Earth's magnetic field is 2*10^-5 T, and the voltage measured from wing tip to wing tip is 4 mV, What is the ground speed of the plane?
To calculate the ground speed of the plane, we need to use the information provided about the wing span, the vertical component of the Earth's magnetic field, and the measured voltage across the wings.
The voltage measured across the wings of the airplane is a result of the electromagnetic induction caused by the interaction between the Earth's magnetic field and the motion of the airplane. This phenomenon is known as the Hall effect.
The Hall effect involves the Lorentz force, which is given by the equation:
F = q * (v x B)
Where:
F = Force
q = Charge
v = Velocity vector
B = Magnetic field
In the case of the airplane flying horizontally, the vertical component of the Earth's magnetic field (B) will be perpendicular to the velocity vector (v) of the airplane. Therefore, we can rewrite the equation as:
F = q * v * B
The measured voltage (V) is directly proportional to the force (F) experienced by the charge (q) crossing the wings of the airplane. Mathematically, we have:
V = F * d
Where:
V = Voltage
F = Force
d = Distance (wing span)
Combining the equations, we have:
V = q * v * B * d
Rearranging the equation to solve for the velocity vector (v), we get:
v = V / (q * B * d)
Substituting the provided values, we have:
v = (4 mV) / (q * (2*10^-5 T) * (20 m))
Now we need to find the value of q, which represents the charge. Unfortunately, the question does not provide information about the magnitude of the charge. Hence, we cannot determine the exact ground speed of the plane without knowing the value of q.
However, once you have the value of q, you can substitute it into the equation above and calculate the velocity vector (v). Keep in mind that the velocity vector represents the magnitude and direction of the airplane's ground speed.