In Exercise 21.29, what is the speed of the electron as it emerges from the field?

Name: Problem 31, Chapter 21: University Physics with Modern Physics
Uploaded: 2019-08-09T06:00:57-08:00
Duration: 5 min 46 s
Channel: Jayashree Behera
Description: In Exercise 21.29, what is the speed of the electron as it emerges from the field?

In Exercise 21.29, what is the speed of the electron as it...

Key Concepts

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.

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.

Transcript

00:01 So the velocity vector is made of two components, x and y components here.

00:10 So we can write the velocity vector like a vector with vx as the velocity along x direction and vy as a velocity along y direction.

00:23 Now the initial velocity, we put a subscript 0 for that.

00:30 And let's say the final velocity is like so.

00:37 Now, we know the magnitudes of the components of the initial velocity.

00:44 So since the initial velocity is completely horizontal, so we have v0x to be equal to 1 .6 times 10 to the par 6 meter per second, that is the magnitude of the total velocity, and v0y is 0 because there is no horizontal component of velocity.

01:00 Now one other thing is since there is no acceleration along the x direction, like acceleration is zero along the x direction, the velocity along this direction remains unchanged from the initial velocity in that direction.

01:21 So the final velocity along x direction will also be equal to the initial velocity along that direction.

01:31 Now the only thing left to find is vy.

01:34 So in order to find that we will use the kinematic equations and we are going to use this equation for our case because this is the simplest one and we already have all the values that we need in order to find this.

01:59 So for the time we can find time by another kinematic equation.

02:12 So we know that x is equal to v0 x times t.

02:21 Oops.

02:23 X is equal to x0 plus v0 x times t so t is equal to x not plus v0 x times t.

02:27 So t is equal to to x minus x0 over v0 x and in exercise 29 this time has already been calculated and it came out to be equal to 1 .25 times 10 to the power minus 8 seconds.

02:56 So we will use this time over here.

03:01 Also v0y is equal to 0.

03:03 So we have vy to be equal to acceleration along y direction times.

03:09 Now this acceleration for an electron, so this has also been calculated in exercise 29, so we know that acceleration, the electric field is equal to force over charge and force by newton's law is mass times acceleration, which gives acceleration to be electric field times charge over mass...

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