Inductance and current

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1. The problem statement, all variables and given/known data

Hey guys.
So, I have the next system in the pic.
It's on the xy plan. the poll moves from left to right with a constant velocity. B=B0*x in z direction and the question is to find the current that goes through the poll.
I've also uploaded what I did but I'm a little confuse about my solution. Does it makes sense that I got that the EMF on the right equals to the EMF on the left? and is the solution correct?

Thanks a lot.


2. Relevant equations



3. The attempt at a solution
 

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