a square loop of side=a has its center at ( 3/2 )a distance away from a infinite wire carrying current . If the loop and the wire are in the same plane initially and then if the loop rotates by 180 degrees then what is the total amount of charge which passes through any point ofvthe loop during rotation? The loop rotates about an axis parallel to the long wire.

what I did is that $q=\int I.dt=\frac {-d\phi}{r.dt}.dt $ and dt cancels so it should be just $\triangle\phi$ which would be final - initial flux giving -2B.A but answer doesn't come by this

where I am thinking wrong

reshown Nov 18, 2016 by Einstein