$10.2.8$ A plane capacitor is placed in a homogeneous magnetic field od induction $B$ parallel to the plates. From point A, electrons enter perpendicularly to magnetic field direction. The tension (voltage) applied to the plates is $V$. What is the condition for which electrons pass through the capacitor?
Electrons pass through capacitor if they don't collide with plates. So, supposing a capacitor of infinite length, electron's velocity must be parallel to the plates (or its horizontal range over a plate greater than its enter's height). This is possible if electric and magnetic forces are in equilibrium (equal absolute values and opposed directions). $$evB = eE$$ $$v = \frac{E}{B}$$ As $E=\frac{V}{h}$, $$\boxed{v = \frac{V}{Bh}}$$ This device is known as speed's selector.
BSc. Luis Daniel Fernández Quintana
Physics Department (FCNE)
Universidad de Oriente, Cuba