Answer
$\mathscr{E} = \frac{3~ \mu_0~i~R^2~\pi~r^2~v}{2x^4}$
Work Step by Step
In part (a), we found that: $\Phi =\frac{ \mu_0~i~R^2~\pi~r^2}{2x^3}$
We can find $\frac{d\Phi}{dt}$:
$\frac{d\Phi}{dt} = \frac{d\Phi}{dx}~\frac{dx}{dt} = (-\frac{3~ \mu_0~i~R^2~\pi~r^2}{2x^4})~(v)$
We can find an expression for the induced emf:
$\mathscr{E} = -\frac{d\Phi}{dt}$
$\mathscr{E} = \frac{3~ \mu_0~i~R^2~\pi~r^2~v}{2x^4}$
