Help with electromagnetism problem

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AI Thread Summary
The problem involves calculating the potential difference between the ends of an airplane's wings, given its wingspan, speed, and the Earth's magnetic field. The key equations for magnetic flux and induced potential difference are provided, emphasizing the need to treat the wings as a rectangular conductor moving through a magnetic field. The main challenge is determining the effective area facing the magnetic field, as only the wingspan is given. The discussion highlights confusion over interpreting the wingspan as either the width or length of the conducting element and the necessity of understanding the plane's motion through the magnetic field. Ultimately, the solution requires recognizing the relationship between the airplane's speed and the magnetic field to find the induced emf.
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Homework Statement



An airplane with a wingspan W = 30 m is flying due north at v = 672 km/h. The Earth's field is 1.210-4 T, due north and inclined q = 42 below horizontal. What is the magnitude of the potential difference between the ends of the wings?
http://media.apexlearning.com/Images/200408/06/ba941605-5eb4-4e21-a8eb-b2cb82a7c95e.gif

Homework Equations



Magnetic flux: φ = B · A · cosθ

Induced potential difference (emf)
due to a changing magnetic field: V = -N · ∆φ/∆t

Motional emf: V = -B · L · v

Could be anyone of these. Also, the problem said to treat it like pulling a rectangular wire through a magnetic field, and find the area facing the field using the angle.

The Attempt at a Solution



It seems this is more of a riddle than a problem. How do I find the area facing the magnetic field? I'm only given the wingspan!
 
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The wingspan gives you the length dimension of conducting rod right? So how can you get the width given the velocity of the plane?
 
Well, the plane is traveling into the field, so I would think the wingspan is the width. So it's the length I don't have. And it's not a conducting rod. The hint said to do the problem as if it was a rectangle circuit, and anyway I don't think there would be any potential difference if it was just a rod.
 
Depending on your setup and how the conducting rod is moving with respect to the magnetic field, you can interpret the wingspan as either the width or length. The term conducting rod is just to relate the situation to a very similar one which you are familiar with.

EDIT: By the way I can't access your picture. It's appears to be "forbidden access".
 
Bah. It's from Apex (Not) Learning. I'll mirror it on Imageshack. Here you go.

http://img401.imageshack.us/img401/892/ba9416055eb44e21a8ebb2cwy2.th.gif

Well whatever the wingspan is, I need another dimension, and Apex is being really anal about not giving me any hints. Would I just use like 1 meter or something?

[gripe] And HOW is this related to the chapter? I don't remember seeing 'riddles' in the curriculum for electromagnetism! [/gripe]
 
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There is already another dimension. The plane is not stationary, it's moving at a constant speed. You need to find the rate at which the conducting wings pass through the magnetic field lines, which would then give rise to a potential difference.
 

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