= Solution
At time $t$, let the centre of the loop have coordinate $Y=d+vt$. With normal $+\mathbf e_x$, the <magnetic flux> is
$$
\Phi_B
=-\int_{Y-a}^{Y+a}\int_{-a}^{a}
\frac{\mu_0I}{2\pi y},dz,dy
=-\frac{\mu_0Ia}{\pi}\log\frac{Y+a}{Y-a}.
$$
<Faraday's law> and <Ohm's law> therefore give a current of magnitude
$$
\boxed{
|I_{\rm loop}(t)|
=\frac{2\mu_0Ia^2v}
{\pi R\bigl((d+vt)^2-a^2\bigr)}}.
$$
The original flux points into the plane and decreases in magnitude as the loop recedes. By <Lenz's law>, the induced current reinforces the into-plane field: it is clockwise when viewed from the $+x$ side.
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