Loop A of radius $r(r<<R)$ moves towards a constant current carrying loop B  with a constant velocity v in such a way that their planes are parallel and coaxial. The distance between the loops when the induced emf in loop A is maximum is

 

Magnetic flux through the loop A; $\phi =B\pi r^2=\frac{{\mu }_{0}I{R}^2}{2{(R^2+x^2)}^{3/2}}\pi r^2$
Induced emf in the loop A; $\epsilon =-\frac{d\phi }{dt}=\frac{{\mu }_{0}I{R}^2\pi r^2}{2}(-\frac{3}{2{(R^2+x^2)}^{5/2}}2x\frac{dx}{dt})$  
                                                $=-\frac{3{\mu }_{0}I{R}^2\pi r^{2}v}{2}\left[\frac{x}{{(R^2+x^2)}^{5/2}}\right]$  
Induced emf is maximum when $\frac{d\epsilon }{dx}=0\Rightarrow (R^2+x^2)-5x^2=0 or x=\frac{R}{2}$