Induced EMF ~ Faraday's Law/Lenz's Law

[Kali8972]

I'm having a lot of trouble with the following questions. I was wondering if someone could steer me in the right direction and tell me what I'm doing wrong.

I suppose my biggest problem is I don't understand how to do these without knowing the number of turns in the coil. Here's what I've done so far:

1. [GianPSE3 29.P.002.] A 20 cm diameter circular loop of wire lies in a plane perpendicular to a 0.80 T magnetic field. It is removed from the field in 0.10 s. What is the average induced emf?

2. [GianPSE3 29.P.005.] A 8.0 cm diameter loop of wire is initially oriented perpendicular to a 1.2 T magnetic field. It is rotated so that its plane is parallel to the field direction in 0.40 s. What is the average induced emf in the loop?

3. [GianPSE3 29.P.006.] A 7.6 cm diameter wire coil is initially oriented so that its plane is perpendicular to a magnetic field of 0.63 T pointing up. During the course of 0.12 s, the field is changed to one of 0.25T pointing down. What is the average induced emf in the coil?

Any help or suggestions would be greatly appreciated! Thanks so much!

Work is in attatched pictures! Thanks!

 

[Hermite]

I've not seen the images but it sounds like each problem is considering 1 loop of wire.

I vaguely remember the following equation:

induced emf = - rate of change of flux = - N x A x B x sin (theta)

N = number of loops
A = area enclosed by loops
B = strength of magnetic field
theta = angle between plane of loop/s and magnetic field

That should be all you need assuming I've remembered the equation correctly.

(Does anyone know how make proper equations in this forum?)

 

[Kali8972]

Hmm.. I don't know why they don't show up

They're located here however:

http://www.pitt.edu/~slm17/problem1.jpg
http://www.pitt.edu/~slm17/problem2.jpg
http://www.pitt.edu/~slm17/problem3.jpg

That helps a lot knowing it's one loop. I was getting really confused on that part. For the area in problems 2 and 3 do you know what I do for it? I'm not sure on the shape so should I just square it?

 

[Hermite]

When they refer to a 'loop', they mean a circular piece of wire so the area is just pi*radius^2 for both 2 and 3 (as far as I can tell).

To find average emf, calculate the beginning emf, the end emf and then average the two results. This will only work if the change in orientation of the loop or the change of field is uniform but that does seem to be the case so it should work just fine.

 

[Hermite]

it looks like the equation you should be using is something like

emf = -(rate of change of flux w.r.t. time)
= -d/dt (NAB sin theta)
= -d/dt (NAB sin (wt))
= -w*NAB cos (wt)

Go to the following link and see page 19:

http://www.cs.ntu.edu.au/homepages/jmitroy/sph102/sect08.pdf

I hope I'm helping more than hindering :)