Question

The diagram shows part of an evacuated tube in which a stream of electrons from an electron gun passes between a pair of parallel large deflecting plates. The vertical displacement of the electron beam as it leaves the parallel plates is ‘x’. (Do not consider gravity and the electron enters the deflecting region parallel to the plates). Which one of A to D below will change the displacement ‘x’ of the beam as it leaves the parallel plate?

(A) increasing the accelerating voltage
(B) increasing the deflecting voltage
(C) increasing the distance between the electron gun and the deflecting plates
(D) increasing the distance between the two deflecting plates

Answer 1

Hint: When the electron enters the parallel deflecting plates, it has acquired some initial velocity due to accelerating voltage. Inside the plates, the force acting upon the electron is due to the deflecting potential. So, we shall see changing what factors shall bring about a change in the displacement (x) of the electron’s path.

Complete answer:
We will check all the options step by step to see their effects on the electron's displacement.
(A) increasing the accelerating voltage: On increasing the accelerating voltage, the speed of the electron's approach towards the deflecting voltage has been increased. Higher speed means the electron stays for a shorter duration of time inside the deflecting plates, hence less displacement and vice versa. Hence, increasing the accelerating voltage will decrease the displacement (x).
(B) increasing the deflecting voltage: On increasing the deflecting voltage, we are applying force along the displacement. Hence, increasing the deflecting voltage will increase the displacement (x).
(C) increasing the distance between the electron gun and the deflecting plates: When the electron is leaving the electron gun, it has already acquired some speed in the horizontal direction. And until it reaches the deflecting plates, no other force acts on it. So, on increasing the distance between the electron gun and the plates will have no effect whatsoever on the displacement (x).
(D) increasing the distance between the two deflecting plates: As we know Electric field is inversely proportional to the distance over which an electric potential is applied. Thus, on increasing the distance, we are decreasing this force, and hence, decreasing the displacement (x).
Hence, from our above analysis, we can conclude that options (A),(B) and (D) are the correct options.

So, the correct answers are “Option A, B and D”.

Note: The above experiment is carried out in a CRT (short for Cathode Ray Tube). A Cathode Ray Tube contains one or more than one electron guns in which images are produced when an accelerated electron beam from the gun strikes on to a fluorescent screen. These are generally used in computer display systems.