Problem 3.373

A proton accelerated by a potential difference $V$ gets into the uniform electric field of a parallel-plate capacitor whose plates extend over a length $l$ in the motion direction. The field strength varies with time as $E=a t,$ where $a$ is a constant. Assuming the proton to be non-relativistic, find the angle between the motion directions of the proton before and after its flight through the capacitor; the proton gets in the field at the moment $t=0 .$ The edge effects are to be neglected.