# Induced Current question

1. Mar 25, 2009

### erinec

1. The problem statement, all variables and given/known data
The rectangular loop shown has resistance 20.0 mΩ.
Determine the induced current in the loop at the instant shown.
http://img264.imageshack.us/img264/7386/picture1nlz.png [Broken]

2. Relevant equations

induced emf = |d(flux)/dt|
I = emf / R

3. The attempt at a solution
I am so lost as to what to do... and I am so desperate.. If you could tell me the steps to solve this question, i would appreciate it very much.

Last edited by a moderator: May 4, 2017
2. Mar 25, 2009

### Staff: Mentor

Show us the Biot-Savart Law (that gives you the B(r) around the wire). Then show us the rest of the solution. I have to give myself an infraction now for giving too big of a hint...

Last edited: Mar 25, 2009
3. Mar 25, 2009

### erinec

Well... the problem is that.. I got this far:

emf = | d(flux)/dt |
= dB * A / dt
= dB (0.04*0.01) / dt
= dB (4*10^-4) / dt

but i do not know how to get dB...;
in other words, i am totally lost.

I have B(r) = u0I/(2*pi*r)

This is my first time seeing this type of question.. and I am very confused as to what I'm doing.

Sorry if it sounds stupid.

4. Mar 25, 2009

### Staff: Mentor

The loop is moving with respect to the wire. So the B(t) through the loop will be changing, since the B is weaker the farther you get away from the wire. Write an equation based on the Biot-Savart Law for the flux throught the loop as a function of radius, and work from there...

5. Mar 25, 2009

### erinec

Which radius should I use? The distance from the wire to the the inner side of the loop or the outer side of the loop?

6. Mar 25, 2009

### Staff: Mentor

You need to integrate over the loop radius.

7. Mar 31, 2011

### bmxicle

I know this is old but i'm working on the exact same question.

So far i have this:
[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Cphi%20%3D%20B%20%5Cbullet%20dA%20%5C%5CB%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20%5Ctextrm%7B%20by%20ampere%27s%20law%7D%20%5C%5C%5Cphi%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%5Cbullet%20dA%20%5C%5C%5Cphi%20%3D%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20L%20dr%20%5C%5C%5Cphi%20%3D%20%5Cint_a%5Eb%20%5Cmu_0%20I/%20%282%20%5Cpi%20r%29%20L%20dr%20%5C%5C%5Cphi%20%3D%20%5Cfrac%7B%20%5Cmu_0%20I%20%5Cln%7B3/2%7D%7D%7B%5Cpi%7D.gif [Broken]

Where the bounds of integration are b = 0.02 and a = 0.03 and L= 4.0cm from the picture. This is where i get lost. I wanted to use faraday's law to use:

[PLAIN]http://www.texify.com/img/%5CLARGE%5C%21%5Ceps%20%3D%20%5Cmid%20%5Cfrac%7Bd%20%5Cphi%7D%7Bdt%7D%20%5Cmid.gif [Broken]

Am i just totally going about this the wrong way by trying to use flux, and i have to use biot savart law?

#### Attached Files:

• ###### (2 -pi r) L dr.gif
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Last edited by a moderator: May 5, 2017