Calculating Induced EMF in a Changing Magnetic Field

AI Thread Summary
The discussion focuses on calculating the average induced EMF in a wire coil subjected to a changing magnetic field. The initial magnetic field is 0.770 T pointing up, and it changes to 0.240 T pointing down over 0.140 seconds. The formula used is E = -N(change in magnetic flux/change in time), but the original calculation was incorrect due to errors in determining the change in magnetic flux and the sign convention. After clarifying that the flux is a vector quantity and correcting the radius used in calculations, the correct average induced EMF is found to be 0.0191 V. The conversation emphasizes the importance of accurately applying vector principles and sign conventions in electromagnetic calculations.
Moxin
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Ok, so here's the problem:

Induced EMF
A 5.80 cm diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.770 T pointing up. During the course of 0.140 s, the field is changed to one of 0.240 T pointing down. What is the average induced emf in the coil?

and here's how i tackled it:

E=-N(change in magnetic flux/change in time)

change in magnetic flux = B2A - B1A = A(B2-B1) = 0.058^2pi(.770 - 0.140)
change in time = 0.140 s

N = 1

So I get..

E= 0.0100 V

Apparently that's wrong. Any suggestions ?
 
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Originally posted by Moxin
... a magnetic field of 0.770 T pointing up.
...
... the field is changed to one of 0.240 T pointing down.
...
... change in magnetic flux = ... 0.058^2pi(.770 - 0.140)
The flux is a vector quantity. Check the B-fields in your equation again.




Originally posted by Moxin
Any suggestions ?
Draw a picture.
 
i thought because they were both perpendicular, jus pointing different directions, it wouldn't matter.. guess i was wrong.. I'm really not sure exactly how to proceed now that i know the flux is a vector quantity since angles aren't given..
 
Originally posted by Moxin
i'm really not sure exactly how to proceed now that i know the flux is a vector quantity since angles aren't given..
You can pretty much just assume that the initial and final vectors are 180 degrees apart. Other than that, don't worry about angles. I sorry for saying "vector," as it probably made you start thinking about oblique directions, sines and cosines and whatnot. That isn't what I wanted to point out. I was trying to draw your attention to the negative sign that you're missing. The flux is a magnitude and sign (which is a 1-D vector). So, pick a sign for up, assign the opposite sign to down, and put the values into the formula accordingly. Your procedure is basically correct; it's the details that are killing you.

Oh what the hell, here's what I get:

0.0191 V ccw

I just noticed something else in your first post. You squared the diameter, but you should square the radius of the loop.
 
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I was going to rush in here to say Nevermind I figured it out but lol I guess I'm too late, and yeh I finally ended up with 0.0191 as well after figuring out I had to add the fields..Thanks anyways mann
 
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