An airplane travel 1000k/h in a region where the Earth's magnetic field is about 5*10-5T.
what is the potential diffenrence induced between the wing tips that are 70 m apart?
v = 10^3 * 1000/3600 meters/second
so
V = potential diff = B L v = 5*10^-5 * 70 * v
To find the potential difference induced between the wing tips of the airplane, we can use Faraday's Law of electromagnetic induction.
Faraday's Law states that the electromotive force (EMF) induced in a conducting loop is equal to the rate of change of the magnetic flux through the loop. Mathematically, it can be expressed as:
EMF = -dϕ/dt
where EMF is the electromotive force, dϕ is the change in magnetic flux, and dt is the change in time.
In this case, the conducting loop is formed by the wings of the airplane, and the magnetic flux through the loop is caused by the Earth's magnetic field.
The magnetic flux is given by the product of the magnetic field strength (B) and the area of the loop (A). Since the wings form a rectangular loop, the area (A) can be calculated as the product of the length (L) and the width (W) of the wings:
A = L * W
Given that the wings are 70 m apart (L = 70 m), we also need to determine the width (W) of the wings.
To find the width, we can consider the speed (v) of the airplane. The speed is given as 1000 km/h, which we can convert to m/s by multiplying by 1000/3600:
v = 1000 km/h = (1000/3600) m/s ≈ 277.78 m/s
To determine the width, we need to know the time it takes for the airplane to travel the distance between the wings. Let's assume it takes Δt seconds.
The width (W) of the wings can be calculated as the product of the speed (v) and the time (Δt):
W = v * Δt
Now, we can determine the magnetic flux (ϕ) through the loop:
ϕ = B * A
Given that the Earth's magnetic field (B) is about 5 * 10^-5T and we have already calculated the area (A) as L * W, we can substitute these values to find ϕ.
Finally, we can calculate the induced potential difference (V) using Faraday's Law:
V = -dϕ/dt
Since we assumed that the width of the wings is determined by the time (Δt), we can rewrite the equation as:
V = -(dϕ/d(Δt))
Now, we have all the information we need to calculate the induced potential difference between the wing tips of the airplane. Substitute the values into the equations and solve for V.