= Solution
Write the wire diameter as $d_w$ to distinguish it from other geometric labels. Its <cross-sectional area> is $A_w=\pi d_w^2/4$, and the total wire length is $4a$. From the <electrical resistivity>, its <electrical resistance> is
$$
R=\frac{4a\rho_c}{A_w}=\frac{16\rho_ca}{\pi d_w^2}.
$$
While the loop straddles the boundary, let $h$ be the height of each vertical side remaining in the <magnetic field>. The linked <magnetic flux> has magnitude $Bah$, with $\dot h=-v$. <Faraday's law> therefore gives $|\mathcal E|=Bav$. Neglecting the loop's <self-inductance>, <Ohm's law> gives
$$
\boxed{I=\frac{Bav}{R}=\frac{\pi d_w^2Bv}{16\rho_c}.}
$$
The into-page <magnetic flux> is decreasing, so <Lenz's law> requires a \b[clockwise] <electric current> as viewed in the diagram. If the loop is wholly inside a uniform <magnetic field>, or wholly outside it, its <magnetic flux> is constant and this induced <electromotive force> is zero. During a rapid transient one should instead solve $L\dot I+RI=Bav$; at the assumed steady speed the same boxed relation holds.
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