Solving Faraday's Law: 0.73V Induced EMF Help Needed

[Bolter]

Homework Statement

Calculate EMF induced on tips of an aircraft wing

Relevant Equations

Faraday's law

I have a simple sketch of the diagram, and I know I must use the vertical component of the magnetic field of the Earth when doing this problem

I got an induced emf of 0.73 volts but I do not know if I correctly substituted the right values into faraday's law equation?

Any help will be really appreciated! Thanks

 

[berkeman]

Seems like a trick question to me. Unless the aircraft is doing aileron rolls, I don't see any change dΦ/dt...

https://www.apstraining.com/wp-content/uploads/2009/10/roll-400x200-c-default.jpg

 

[etotheipi]

I agree with the answer you gave, though I think you're supposed to treat the wingspan as a conducting rod. Like @berkeman mentioned, there isn't a rate of change of flux linked in the actual wing, only the flux linked in an imaginary loop like below:

We then have $\varepsilon = B_{v}lv$ where the three terms are mutually orthogonal.

 

[Bolter]

Seems like a trick question to me. Unless the aircraft is doing aileron rolls, I don't see any change dΦ/dt...

https://www.apstraining.com/wp-content/uploads/2009/10/roll-400x200-c-default.jpg

View attachment 257343

So if there is no change in dΦ/dt, then the emf induced is zero?

 

[berkeman]

The Lorentz Force will exert forces on the electrons in the wing material, so maybe there is a way to calculate the voltage generated that way. The force due to qv X B will be balanced by qE, so there will be an electric field pointing along the wing. That will generate a small voltage, but I don't think you can use dΦ/dt to do the calculation, since Φ is not changing.

 

[berkeman]

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genwir2.html

 

[Bolter]

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/genwir2.html

View attachment 257345

So I managed to do this now and it lead me to this as my induced voltage

But this gives me the same answer that I had when I had used dΦ/dt = V?

 

[berkeman]

Do you get that same answer when you use the Hyperphysics calculator that I linked?

 

[Bolter]

Do you get that same answer when you use the Hyperphysics calculator that I linked?

Yes :)

 

[rude man]

... I don't think you can use dΦ/dt to do the calculation, since Φ is not changing.

I second that. In general it is dangerous to apply maxwell' s equations (which is what Farady's law is based on) to moving media.
The correct way is to use the Blv law which is what @berkeman stated.