Question

An electron is in motion at 4.0 × 106 m/s horizontally when it enters a region of space between two parallel plates, as shown, starting at the negative plate. The electron deflects downwards and strikes the bottom plate. The magnitude of the electric field between the plates is 4.0 x 102 N/C and separation between the charged plates is 2.0 cm. Determine the horizontal distance travelled by the electron when it hits the plate.

Answer 1

xmax = 9.5cm

Step-by-step explanation:

In this case, the trajectory described by the electron, when it enters in the region between the parallel plates, is a semi parabolic trajectory.

In order to find the horizontal distance traveled by the electron you first calculate the vertical acceleration of the electron.

You use the Newton second law and the electric force on the electron:

`F_e=qE=ma` (1)

q: charge of the electron = 1.6*10^-19 C

m: mass of the electron = 9.1*10-31 kg

E: magnitude of the electric field = 4.0*10^2N/C

You solve the equation (1) for a:

`a=(qE)/(m)=((1.6*10^(-19)C)(4.0*10^2N/C))/(9.1*10^(-31)kg)=7.03*10^(13)(m)/(s^2)`

Next, you use the following formula for the maximum horizontal distance reached by an object, with semi parabolic motion at a height of d:

`x_(max)=v_o\sqrt{(2d)/(a)}` (2)

Here, the height d is the distance between the plates d = 2.0cm = 0.02m

vo: initial velocity of the electron = 4.0*10^6m/s

You replace the values of the parameters in the equation (2):

`x_(max)=(4.0*10^6m/s)\sqrt{(2(0.02m))/(7.03*10^(13)m/s^2)}\\\\x_(max)=0.095m=9.5cm`

The horizontal distance traveled by the electron is 9.5cm