In a cathode-ray tube, a beam of electrons is projected horizontally with a speed of 1.0x109 cm/s into a region between a pair of horizontal plates 2.0 cm long. an electric field between the plates causes a constant downward acceleration of the electrons of magnitude 1.0x1017 cm/s2. find (a) the time required for the electrons to pass through the plates, (b) the vertical displacement of the beam in passing through the plates, and (c) the components of the velocity of the beam is it emerges from the plates.

(a)

The time it takes for the electron to pass through the plates depends only on its horizontal motion,

The horizontal motion is a uniform motion, with constant velocity

The total distance travelled by the electron to pass through the plates is

d = 2.0 cm

Using the equation for uniform motion,

where t is the time taken. Solving for t,

(b) -0.2 cm

The vertical motion of the electron is a uniform accelerated motion, so the vertical displacement is given by

where

is the initial vertical velocity

is the acceleration (negative because it is downward)

We can write that

Since the electron initially travels horizontally, and so if we substitute the time we found in part (a), we can find the vertical displacement after the electron has passed through the plates:

(c)

The horizontal component of the velocity of the beam does not change, since the there are no forces acting in the horizontal direction, so it remains

Instead, the vertical component of the velocity changes according to the equation

And substituting the values we found for a and t, we find

where the negative sign indicates the downward direction.