A helicopter has blades if 3m, rotating at 2rev/s about a central hub. If the vertical components of the Earth's magnetic field is 0.5x10–4 T, what is the emf induced between the blade tips and the central hub.
To find the emf induced between the blade tips and the central hub, we can use Faraday's Law of electromagnetic induction. This law states that the emf (ε) induced in a conductor is proportional to the rate of change of magnetic flux through the conductor.
The magnetic flux through the conductor can be calculated by multiplying the magnetic field (B) by the area (A) through which the magnetic field passes. In this case, the area is the circular surface formed by the rotating blades.
The formula for the magnetic flux (Φ) is given by:
Φ = B * A
The area (A) of a circle can be calculated using the formula:
A = π * r^2
where r is the radius of the circle.
Given:
Blade length (radius) = 3m
Rotation rate = 2 rev/s
Vertical component of the Earth's magnetic field (B) = 0.5 x 10^(-4) T
First, we need to calculate the area (A) of the circular surface formed by the blades:
A = π * r^2
= π * (3m)^2
= 9π m^2
Next, we need to calculate the rate of change of magnetic flux (dΦ/dt) to find the induced emf (ε). Since the magnetic field is constant and the blades are rotating at a constant rate, dΦ/dt is simply the product of the constant magnetic field and the area of the circular surface:
dΦ/dt = B * A
= (0.5 x 10^(-4) T) * (9π m^2)
Finally, we can calculate the induced emf (ε) using Faraday's Law:
ε = -dΦ/dt
= -(0.5 x 10^(-4) T) * (9π m^2)
Calculating this multiplication gives the answer.