Answer
${\bf 159}\;\rm A/s$
Work Step by Step
Let's assume that the resistance of the solenoid is zero and it is an ideal one at which the magnetic field at any instant is the same everywhere within the solenoid.
Recalling that
$$E=\dfrac{r}{2}\left| \dfrac{dB}{dt}\right|$$
where $B=\dfrac{\mu_0 NI}{l}$ where $N/l=n$, so
$$E=\dfrac{\mu_0 n r}{2}\left| \dfrac{d I }{dt}\right|$$
Hence,
$$\left| \dfrac{d I }{dt}\right|=\dfrac{2E}{\mu_0 n r}$$
Plug the known;
$$\left| \dfrac{d I }{dt}\right|=\dfrac{2(5\times 10^{-4})}{(4\pi\times 10^{-7})(1000)(0.5\times 10^{-2})}$$
$$\left| \dfrac{d I }{dt}\right|=\color{red}{\bf 159}\;\rm A/s$$
