These questions are about an electron gun.Thank you, I will definitely rate:))

1. Kinematic analysis: The electrons arrive at the deflection plates with a velocity vx along the x-axis. The width of the plates (along the x-axis) is L. The time it takes to pass this distance is: At1 = ( symbols L and Vx) During this time interval, the electrons experience a constant acceleration a, along the y-axis, due to the electric field. Their velocity along the y-axis at the end of this interval is: Vy = ay At1 = ( symbols ay, L and Vx) It now continues a distance D along the x-axis with no acceleration. The time it takes to travel this distance is: At2 = (symbols D and Vx) During this time, it will have traveled a distance Y along the y-axis given by: ( multiply equations (2) and (3) together ) Y =v,At2 = (symbols ay, D, Vx and L) We now have an expression for Y in terms of the acceleration a, and velocity vx. 2. Relation to electrical properties: Now we relate the kinematic quantities a, and vx to the electrical properties , and V. of the CRT. a) vx depends on V. . The kinetic energy of the electron, after being accelerated through the potential difference Va, of the electron gun is equal to the change in potential energy. Therefore start with the equation K= UE, and solve for vx2 : Vx 2 = ( symbols me, qe and Va) b) a, depends on Va . The force on an electron between parallel plates seperated by a distance d and voltage Va is ( hint: F is related to E, and E is related to Va and d ) F = (symbols qe, Va and d) This means that the acceleration a, can be expressed as ay = F/me = (symbols qe, Va and d and me) 3. Final result Rewrite relation (4) by i: using (7) to get rid of dy and ii: using (5) to get rid of vx2 . Final result: Y = (symbols L,D,d, Va and Va) Bonus: (8) is the deflection that occurs while the electrons travel the distance D. The electrons are also deflected an additional (but small) amount as they first travel over the distance L. Show that, if we take this into account, we would get the following expression for Y: L Vd Y =(D+4/2) 2d Va