Problem $3$: Electrons with charge $-e$ and mass $m$ are emitted from the cathode $C$ and accelerated toward slit A with different speeds in the direction shown. The electrons enter a region with a downward pointing electric field $($magnitude $E)$ and a magnetic field $($magnitude $B)$ that points into the plane of the figure. Gravity can be ignored in this case. If the electrons travel on a straight trajectory through the gap between the plates, what is their speed? Write your answer in terms of some or all of the following: $e,m,E,$ and $B.$

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