# Homework Help: Expression for induced ε from reducing Loop

1. Dec 11, 2008

### quietriot1006

1. The problem statement, all variables and given/known data

A circular loop made from a flexible, conducting wire is shrinking. Its radius as a function of time is . The loop is perpendicular to a steady, uniform magnetic field B .
Find an expression for the induced ε in the loop at time t.
Give your answer in terms of , , t, B and appropriate constants.

2. Relevant equations
Magnetic Flux (Φm)=A*B
I(induced) = ε / R
ε =Absolute value of (dΦ/dt)

3. The attempt at a solution
At first get the magnetic flux using the Area * Magnetic field. Area is (pi)r^2 * B. I use this in faradays law with dt but i dont get the write expression. I end up getting

ε(t)=(B(pi)(r_0*e^(beta*t))^2)/t

I know im differentiating somewhere wrong but i dont know where.

Last edited by a moderator: Apr 16, 2017
2. Dec 11, 2008

### Redbelly98

Staff Emeritus
What's the derivative of

f(t) = eat

3. Dec 11, 2008

### quietriot1006

Wouldnt that just be a'(t)e^at?

4. Dec 11, 2008

### Redbelly98

Staff Emeritus
Uh, no. I meant for "a" to be a constant, sorry about the confusion.

If you can express r2 in the form:

r2 = ro2eat,​

and if you can take the derivative of eat correctly, then you'll be able to figure out what dA/dt is.

5. Dec 11, 2008

### quietriot1006

wouldn't the derivative of f(t)=e^at be just (1/a)e^at? im not really sure and i dont understand how you were able to square the equation?

6. Dec 11, 2008

### Redbelly98

Staff Emeritus
No, the derivative is
a eat

You'll have to figure out an expression for A, using A=∏r2, and differentiate it. I mentioned the whole eat thing because the expression for A could be put in that form.

It sounds like you're having trouble remembering calculus ... has it been a while since you took it?