# Induced Emf in Rectangular Loop Problem

1. Jun 15, 2011

### ethanabaker1

1. The problem statement, all variables and given/known data
"You push a rectangular loop of width .2m, length .8 m, and resistance R=200$\Omega$ into a magnetic field (out of page) Bout=.4 T and a speed v=.2 m/s. The long side of the rectangle is parallel to the x axis. What is the current flowing in the loop?"

2. Relevant equations

I think I should use:
Emf=vBl
Ohm's Law - $\Delta$V=IR
3. The attempt at a solution
Using the equation emf=vBl, I did emf=(.02)(.8)(.4)=.0064.
Then I said that emf=$\Delta$V, so using Ohm's Law I did $\frac{.0064}{200\Omega}$ and got 3.2 x 10-5 A as my answer.

My problem is that the only problems we've worked are for circular loops and I'm not sure what length to use for l.

2. Jun 16, 2011

### Andrew Mason

$$emf = \oint \vec{E}\cdot d\vec{s} = \frac{d\phi}{dt} = B\frac{dA}{dt}$$

All you have to do is work out dA/dt, the rate of change of the area enclosed by the loop. If l is the distance along the x axis through which you have pushed the loop and w is the width of the loop what is dA/dt?

AM

3. Jun 16, 2011

### ethanabaker1

How would I do this algebraically?

4. Jun 16, 2011

### Andrew Mason

Since dA = wdx and w is constant, then dA/dt = w(dx/dt) = wv

So emf = Bwv

AM