A $160-$VV battery is connected across two parallel metal plates of area $28\mathrm{.}5$ cm$2$cm$2$ and separation $8\mathrm{.}30$ mm$.$ A beam of alpha particles $($charge $+2$e$,$ mass $6\mathrm{.}641027$kg$)$ is accelerated from rest through a potential difference of $1\mathrm{.}60$ kV and enters the region between the plates perpendicular to the electric field. What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?