Question

An electron is projected with an initial speed Vo = 5.35x10^6 m/s into the uniform field between the parallel plates. The direction of the field is vertically downward, and the field is zero except in the space between the two plates. The electron enters the field at a point midway between the plates.

Length of the plates= 2cm
Distance between the plates= 1cm
If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field.

Answer 1

E = 3.04 10⁻⁵ N / C

Step-by-step explanation:

In this problem we can use the kinematics to find how long it takes the electron to travel the plates

Let's start by reducing the magnitudes to the SI system

vₓ = 5.35 10⁶ m / s

x = 2 cm = 2 10⁻² m

y = 1 cm = 1 10⁻² m

x = vₓ t

t = x / vₓ

t = 2 10⁻² / 5.35 10⁶

t = 3,738 10⁻⁹ s

This time is also the time it takes for vertical movement to go from the center to the plate, let's look for acceleration with Newton's second law

F = m a

a = F / m = e E / m

y =
`v_(oy)` + ½ a t²

`v_(oy)` = 0

We replace

y = ½ e / m E t²

E = 2 y m / e t²

Let's calculate

E = 2 1 10⁻² 9.1 10⁻³¹ / (1.6 10⁻¹⁹ 3,738 10⁻⁹)

E = 18.2 10⁻³³ / 5.98 10⁻²⁸

E = 3.04 10⁻⁵ N / C