magnetics

find the change in magnetic flux and use the relation

charge\,\: passed= \frac{\Delta \Phi}{R}

select an element ∂x on either side of square at a distance x from the wire
now φ=B.A
=∫μ_oi2πx.l∂x
=μ_oil2π∫∂xx
vary integral frm 0 to 2l
we get
φ=μ_oil ln22π
now e=-∂φ∂t
→ i=eR
q=i∫∂t
q=μ_oil ln22πR