Each of the electrons in a particle beam has a kinetic energy of 1.60 ×10^-17 J . (a) What is th

Each of the electrons in a particle beam has a kinetic...

Key Concepts

Electron Dynamics

Electron dynamics involves studying the motion and behavior of electrons under the influence of forces, particularly electric fields. It covers how electrons gain or lose kinetic energy, respond to electric forces, and how external fields can control their trajectories. This concept is central to understanding experiments and technologies involving particle beams and charged particle motion.

Electric Force on Charged Particles

The electric force on a charged particle in an electric field is given by the product of the charge and the electric field strength. This concept explains how particles like electrons, which possess a negative charge, experience acceleration or deceleration when they move through an electric field, thereby affecting their motion and energy.

Uniform Acceleration and Kinematics

When a constant force acts on a particle, the resulting acceleration is constant, and the equations of kinematics can be applied. These equations help to relate initial velocity, final velocity, acceleration, distance, and time. This is essential in problems involving deceleration of particles, such as calculating the time it takes for electrons to come to a stop under a uniform electric field.

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to its change in kinetic energy. In the context of charged particles moving in an electric field, this principle allows us to relate the work done by the electric force over a distance to the kinetic energy loss of the particle, providing a way to calculate parameters like the required electric field strength or stopping distance.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. For charged particles like electrons, knowing their kinetic energy helps in understanding the work that must be done to change their speed or bring them to rest. This concept is fundamental in analyzing energy transfer processes in physics.

Uniform Electric Field

A uniform electric field is characterized by a constant magnitude and direction throughout the region of interest. It exerts a constant force on charged particles. Understanding uniform electric fields is crucial in analyzing how charged particles, such as electrons, accelerate or decelerate, and is a key concept in electrostatics and charged particle dynamics.

Transcript

00:01 For this problem on the topic of electric forces and fields, we are told that an electron beam has a kinetic energy of 1 .6 times 10 to the minus 17 joules.

00:09 That's for each of the electrons in this beam.

00:12 We want to use this information to calculate the magnitude of the uniform electric field that will stop these electrons in 10 centimeters.

00:20 Then we want to know the time it will take for the electrons to come to rest, and we want to know what the electrons will do once they do come to rest.

00:29 Now, when an electron, which is a negative charge, moves a distance delta x in the direction of electric field, the work done on the electron w is equal to the electric force applied to the electron times delta x times cosine theta, where theta is the angle between the applied force and the displacement of electrons.

00:56 And this is equal to the charge on the electron, little e times the electric field strength e, which gives us the force times the distance delta x.

01:10 And this case, the electron is negatively charged, so the angle is 180 degrees.

01:19 So this gives us minus e times the electric field strength e times the distance delta x.

01:28 Now, from the work energy theorem, we have that minus e, e delta x, your kinetic energy theorem, rather, is equal to minus the initial kinetic energy of the electrons, which is k -e, which means that the electric field strength, e, is equal to the initial kinetic energy of the electrons divided by the charge of the electron times delta x.

02:04 And now we have an equation that relates the electric field with the distance.

02:08 And so we know the kinetic energy of each electron to initially be 1 .6 times 10 to the minus 17 joules divided by the charge of an electron 1 .6 times 10 to the minus 19 kuloms and the distance is 0 .1 meters, which is 10 centimeters.

02:39 And so the electric field strength that is required is 0 .1 meters.

02:44 1 times 10 to the power 3 newton's column...

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