Calculating Induced EMF in a Changing Magnetic Field

[Moxin]

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 ?

 

[turin]

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.

 

[Moxin]

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..

 

[turin]

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.

 

[Moxin]

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