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

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Homework Help Overview

The discussion revolves around applying Faraday's Law to calculate the induced electromotive force (EMF) in a scenario involving an aircraft's wingspan and the Earth's magnetic field. Participants are exploring the conditions under which EMF is induced and the relevance of changing magnetic flux.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of Faraday's Law and question whether the induced EMF can be calculated given the conditions described. Some express uncertainty about the relevance of changing magnetic flux and whether the wingspan can be treated as a conducting rod.

Discussion Status

The conversation is ongoing, with various interpretations being explored. Some participants suggest that the scenario may be misleading, while others propose alternative methods for calculating the induced voltage, such as using the Lorentz Force. There is no explicit consensus on the correct approach yet.

Contextual Notes

Participants are considering the implications of the aircraft's motion and the nature of the magnetic field. There is a mention of potential constraints regarding the assumptions made about the system, particularly in relation to the rate of change of magnetic flux.

Bolter
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Homework Statement
Calculate EMF induced on tips of an aircraft wing
Relevant Equations
Faraday's law
Screenshot 2020-02-19 at 17.38.38.png

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

IMG_3901.JPG


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
 
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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:

1582134921795.png


We then have ##\varepsilon = B_{v}lv## where the three terms are mutually orthogonal.
 
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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.
 
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Do you get that same answer when you use the Hyperphysics calculator that I linked?
 
berkeman said:
Do you get that same answer when you use the Hyperphysics calculator that I linked?

Yes :)
 
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  • #10
berkeman said:
... 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.
 
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