What is the emf induced in the looop?

[mr_coffee]

An elastic conducting material is stretched into a circular loop of 11.0 cm radius. It is placed with its plane perpendicular to a uniform 0.900 T magnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 80.0 cm/s. What emf is induced in the loop at that instant?

I used:
EMF = - d(change in mag flux)/dt
EMF = - (.900)(.11)^2*PI*5.027 rad/sec = -.17198, i also tried the positive version of that, both wrong. Any ideas why? Thanks.

 

[mezarashi]

What level course is this for? I think you may be expected to do calculus. d/dt on the changing Area which is a function of circumference.

 

[mr_coffee]

This is college level, so yes calculus is doable. So your thinking I should take the derivative of somthing?

d/dt on the changing Area which is a function of circumference.

can you expand on this alittle? For one problem I did take the derivative to get the right answer but it was actually looking like a function and it had the variable t in it...like:
The magnetic flux through the loop shown in Figure 30-35 increases according to the relation B = 6.0t2 + 7.6t, where B is in milliwebers and t is in seconds.
I took the derivative of B and then plugged in the given time to find the EMF induced at a certian time. But i don't see how I'm going to come up with a function expression in this problem. But i may not see somthing you do. THanks!

 

[mezarashi]

You need to always consider what is causing the change in flux. Now usually to make things simple, they always have either only the area or the magnetic field intensity changing. Then:

$$EMF = -\frac{d \Phi_{flux}}{dt} = -A\frac{dB}{dt}$$

or

$$EMF = -\frac{d \Phi_{flux}}{dt} = -B\frac{dA}{dt}$$

.

If, dA/dt or dB/dt is directly given to you, then that makes things simple. Otherwise, you must write out a function for the area or field, then differentiate that function accordingly.