Electromagnetic Induction Question

[Erwin Schrodinger]

A helicopter has 4 rotor blades attached to the central axis of rotation. (Like a + sign with the axis of rotation at the center.)

Each rotor blade is 5.2m long and spins at 6 revolutions per second perpendicular to the Earth's magnetic field of 0.047T. What is the emf induced between the axis and the tip of a rotor blade?

This is what I did.

The tip of a rotor blade sweeps out a circular path so:

v = 2πr/T = 2πrf = 2π(5.2)(6) = 196.035m/s

emf = Blv = 0.047(5.2)(196.035) = 0.048V


A friend of mine had this solution.

Φ = BA = 0.047π(5.2)^2 = 0.004Wb

emf = -N∆Φ/∆t = -N∆Φf = -1(0.004)(6) = 0.024V


I told him his solution didn't work because he is using the area of the entire circular path instead of the area of the blade (which cannot be calculated by the way). Also he is using the initial flux as the change in flux which isn't correct either. So who is right? Or are we both wrong?

 

[berkeman]

To get a net EMF from the line integral around a closed path, the amount of magnetic flux through the closed path's surface has to be changing. I don't get how you have a changing flux with this geometry... Am I missing it? Now if you had a single magnet that each blade was passing over, then sure, the change in the flux (first one way and then the other) would induce an EMF and the resulting eddy currents would impede the progress of the blades.

Come to think of it, the answer is almost certainly zero. Can you think of why? What are helicopter blades typically made of?

 

[daniel_i_l]

If you want to get the right answer with your blv method you have to divide the speed by 2 because you need the average speed of the blade, not just the tip.

 

[berkeman]

Let's see... What's one half of zero...