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.