Contracting Loop in a Magnetic Field

[Angie K.]

Homework Statement

An elastic circular loop in the plane of the paper lies in a 0.81 T magnetic field pointing into the paper. If the loop's diameter changes from 19 cm to 6.8 cm in 0.45 s,

a. what is the magnitude of the average induced emf?

b. If the loop's resistance is 2.3 Ω, what is the average induced current I during the 0.45 s?

Homework Equations

emf = change in flux * B / change in time

magnetic flux = B*A cos Theta

The Attempt at a Solution

Using the equation from above,

the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

= 3.7875*10^-2 T/m^2

emf = (3.7875*10^-2 T/m^2) / 0.45s = 8.4167*10^-2 Volts

Which is wrong but I am not sure where I went wrong.
Maybe something with the distance? Because I feel like that's the one place where I could have messed up...

Thanks in advance!

 

[BiGyElLoWhAt]

You made a mistake here:

the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

You need to calculate the change in area, not the change in diameter.
You want this: $\Delta A = A_{final}-A_{initial} = \pi r_{final}^2-\pi r]_{initial}^2$
Try that and see if it works.

 

[TSny]

the distance that I am going to use is .19m - .068m = .122 m (change in distance)

magnetic flux = (0.81T)(pi)(0.122m)^2 cos 0

This is where the mistake is. Try finding the initial total flux and then the final total flux (after 0.45 s). Use these to get the change in flux.

[You can ignore my post. BiGyElLoWhAt already posted]

 

[BiGyElLoWhAt]

Beat you ;)

 

[TSny]

Beat you ;)

 

[Angie K.]

You made a mistake here:You need to calculate the change in area, not the change in diameter.
You want this: $\Delta A = A_{final}-A_{initial} = \pi r_{final}^2-\pi r]_{initial}^2$
Try that and see if it works.

Beat you ;)

For initial flux : .81T (pi*r (.19^2) = 9.18633e-2
For final flux: .81T (pi*r (.068^2) = 1.17666e-2

so the change in flux is 1.17666e-2 - 9.18633e-2 = - .0800967

so I plug that into find Emf:

magnitude of emf (- .0800967/0.45s) and it still isn't the right answer.

 

[TSny]

For initial flux : .81T (pi*r (.19^2) = 9.18633e-2
For final flux: .81T (pi*r (.068^2) = 1.17666e-2

so the change in flux is 1.17666e-2 - 9.18633e-2 = - .0800967

so I plug that into find Emf:

magnitude of emf (- .0800967/0.45s) and it still isn't the right answer.

Looks good except you need to interpret the word "magnitude".

 

[Angie K.]

Looks good except you need to interpret the word "magnitude".

Beat you ;)

I got the right answer for both parts. Thanks to you both for the help!