Induced current in a square coil by a current-carrying wire

[greg_rack]

Homework Statement

Consider the situation below.
The wire carries a current $I(t)$ decreasing with time, in the direction $-\hat{y}$. In which direction is the induced current moving in the conductive square coil?

Relevant Equations

Faraday-Neumann-Lenz's law

I'll try to explain to you my thinking behind this problem... tell me if it's correct or not.
In short, I have assumed the area enclosed between the wire and the left side of the coil to be $A$ in which is present a $-\hat{z}$ field, and noticed that the flux it generates must be canceled by that in the $+\hat{z}$ direction present immediately at the right of the wire, enclosed in the same $A$ area.
Now, all we are "left" with, is the area to the very right of the coil, with a $+\hat{z}$ decreasing(since $I$ is decreasing) field which contributes to the total flux of the coil; for FNL's law, this will create an induced EMF and hence a current in the counter-clockwise direction.

Am I correct?

 

[TSny]

Yes, that's correct. Your analysis is very good.

 

[greg_rack]

Yes, that's correct. Your analysis is very good.

That's great, thank you very much!