Why Does Using A=L^2/4 Lead to Incorrect Results in Calculating EMF in a Loop?

[pokemon123]

Homework Statement

AP Physics C E and M 2

Relevant Equations

emf=d(flux)/dt

I am attempting to solve part b of this question. I start with the equation A=L^2/4 and I get dA=L/2(dl). Next I find dA/dt=L/2(dL/dt) and I realize dL/dt=v. Thus I get -d(flux)/dt=-BLv/2. Finally, I use emf/R=I. I get -BLv0/2R=I. However, the answer is BLv0/4R=I. I understand dA is supposed to equal L/4(dl) but I am confused why starting with the function A=L^2/4 gets me the wrong answer.

 

[Doc Al]

I start with the equation A=L^2/4

That's the full area of the wire loop. What you want is the area that is in the magnetic field, which will give you the flux through that loop. Think (L/4)*x.