In Exercise 21.27 , what is the speed of the electron as it emerges from the field?

Name: Problem 28, Chapter 21: University Physics with Modern Physics
Uploaded: 2021-05-21T17:50:55-08:00
Duration: 6 min 1 s
Channel: Laszlo Zalavari
Description: In Exercise 21.27 , what is the speed of the electron as it emerges from the field?

In Exercise 21.27 , what is the speed of the electron as it...

Key Concepts

Charged Particle Dynamics

The motion of charged particles in an electric field is governed by the force exerted on them by the field. This fundamental concept explains how an electron accelerates and gains speed as it is subjected to the forces within the field, typically summarized by equations that link electric forces to acceleration.

Energy Conservation

This principle states that the total energy remains constant in an isolated system. In the context of a charged particle moving through an electric field, the loss of electric potential energy is converted into kinetic energy, which defines the particle's speed as it exits the field.

Work-Energy Principle

The work performed on a charged particle by an electric field is transferred into kinetic energy. For an electron, the energy gained from the field (often expressed in terms of a potential difference) directly translates into an increase in its velocity, allowing us to compute its speed using energy relations.

Transcript

00:01 Hello, everyone.

00:01 In this problem, we're asked to find the final speed of an electron that goes through an electric field that is pointed horizontally or perpendicularly to its initial direction of travel.

00:14 So here's the situation.

00:16 Initially, the electron has a speed of 1 .60 times 10 to 6 meters per seconds.

00:23 And it's going into, it's going, it's entering halfway between two plates that produce a, uniform electric field pointing downwards.

00:33 So the initial speed or the initial velocity of the electron is perpendicular to the field is pointing horizontally.

00:41 So this is a right angle over here.

00:44 We know that the plates have dimensions that their separation is one centimeter and its width or the width of the plates is two centimeters.

00:54 So how do we find the final speed? well, we know that since the electric field is pointing perpendicular to the x direction.

01:04 We know the electric field is not going to be producing or changing.

01:08 It's not going to be producing any acceleration in the x direction.

01:11 So it's not going to change the x component of the velocity of the electron.

01:15 However, it is going to accelerate the electron in the y direction.

01:20 So this is the y direction up that way, and this is the x direction to the right.

01:28 So since the electron is entering halfway between, that's going to be one of the important details that we're going to use.

01:35 But first we need to find actually how much time the electrons spins inside this electric field.

01:40 Because we need to know for how long it's going to be accelerating, and only then can we actually find the final speed.

01:47 So what we do first is we have to first find at the time that the electron spans of the electric field.

01:52 Now, we know that this is going to be given by the fact that the electron is just missing this top plate.

02:02 So it's, you know, the direction or the time it spends is just about enough to go all the way to the end of this plate over here.

02:14 So how much, basically, the question is, how long does it take the electron to cover this horizontal distance of two centimeters? so the width is going to be the electrons speed times the time it spans in the electric field.

02:29 And so rearranging that for the time, we find that the time is the width divided by the initial x speed or the initial x velocity.

02:37 And we find that that to be equal to 1 .25 times 10 to the minus 8 seconds.

02:43 So that's basically the first part of the calculation.

02:46 So now we know that the electron spans 1 .25 times to minus 8 seconds, really, really short amount of time...

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