Calculating Induced Current in a Rectangular Loop

[shannon]

Homework Statement

A WxH rectangular loop of wire, with resistance R, lies on a table a distance s from a separate long straight wire carrying a current I.
If the loop is pulled to the right, parallel to the wire, with the speed v, then what is the magnitude of the current induced on the loop?

Homework Equations

The Attempt at a Solution

I found that (a distance r away)
dφ=B•dA=(µₒI/2π)Wdr
now, to find φ
φ=(µₒI/2π)∫dr/r
I'm not sure about these limits...I was thinking from W->W+c (where c is just a constant)
But I'm not sure...
From here I was going to use the equations:
ε= -dφ/dt
I=ǀεǀ/R

 

[alphysicist]

Hi shannon,

Homework Statement

A WxH rectangular loop of wire, with resistance R, lies on a table a distance s from a separate long straight wire carrying a current I.
If the loop is pulled to the right, parallel to the wire, with the speed v, then what is the magnitude of the current induced on the loop?

Homework Equations

The Attempt at a Solution

I found that (a distance r away)
dφ=B•dA=(µₒI/2π)Wdr
now, to find φ
φ=(µₒI/2π)∫dr/r
I'm not sure about these limits...I was thinking from W->W+c (where c is just a constant)
But I'm not sure...
From here I was going to use the equations:
ε= -dφ/dt
I=ǀεǀ/R

Was there more information given? I think it matters which side of the rectangle is parallel to the long wire.

Also, I think it would be better to consider this as a motional emf problem rather than directly calcuating the loop flux. Does that help?