A simple and common technique for accelerating electrons is...

A simple and common technique for accelerating electrons is shown in Figure 18.55 , where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electron if the field strength is $2.50 \times 10^{4} \mathrm{N} / \mathrm{C}$ (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.

A simple and common technique for accelerating electrons is shown in Figure 18.55 , where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to
continue moving. (a) Calculate the acceleration of the electron if the field strength is $2.50 \times 10^{4} \mathrm{N} / \mathrm{C}$ (b) Explain why the electron will not be pulled back to the positive plate
once it moves through the hole.

Key Concepts

Motion of Charged Particles

The motion of charged particles in electric fields encompasses the study of their trajectories, acceleration, and velocities as influenced by electrostatic forces. This concept is central to disciplines such as electromagnetism and particle dynamics, describing how particles continue moving under specific initial conditions and field configurations.

Newton's Second Law of Motion

Newton's second law, expressed as F = ma, links the net force acting on an object to its acceleration and mass. In the context of charged particles, it provides a method to calculate acceleration from the electric force, forming the basis for analyzing motion under the influence of electric fields.

Electric Force on a Charge

The force experienced by a charge in an electric field is given by the equation F = qE, where q is the charge and E is the electric field strength. This fundamental relationship is crucial for determining the dynamics of charged particles when they are exposed to an electric field.

Uniform Electric Field

A uniform electric field is defined as a region where the strength and direction of the electric field remain constant. It is an essential concept for understanding how forces act on charged particles over a given area, leading to predictable motion and acceleration when subjected to this field.

Transcript

00:01 To solve this exercise, we have to recall just a few things regarding the electric field and the electric force.

00:08 So starting with the electric force, what we have to remember is that the electric force is the electric field times the charge that is under this electric field.

00:23 And what we have to remember about the electric field is that the field generated by the electric field, a uniformly charged and infinite plate.

00:35 Suppose we have this plate here, that has a total positive charge, for instance.

00:43 The electric field is going to be constant.

00:46 So this is what you have to remember, is that the electric field generated by this is constant.

00:53 That means that the electric field won't change its value, no matter how far you are from the plate.

01:02 And if the plate is positive, we have that the electric field is going to point outwards from the plate, and it's always going to be perpendicular to the surface of the plate.

01:18 So this is the electric field generated by this type of charged body.

01:27 Okay, this is the only thing that we have to remember, because in this exercise, we're going to suppose that we're going to try to accelerate an electron by using some infinite plates.

01:39 So we're going to use one negatively charged infinite plate in the left side and a positive infinite plate on the right side.

01:52 And this positive plate will have a small hole through which the electron can pass.

02:02 And we have an electron here.

02:09 Okay? so the exercise tells us that the electric field in between the two plagues, this electric field, so let me draw here, is going to be, has a strength of 2 .5 times 10 to the 4 newton per kilogram.

02:39 And in question a, we want to calculate what is going to be the acceleration of this electron due to this electric field.

02:49 So we know that this electric field is constant because the electric field generated by each plate is constant.

02:59 Okay? now, using this formula, we have that the electric force, that is the only force acting on the electron that is making the electron.

03:12 Electron move to this direction is the electrons charge times the electric field.

03:22 And since this is the net force acting on the body, we can use newton's second law and make this equal to the mass of the electron times its acceleration.

03:32 So the acceleration is going to be the electrons charge, which is 1 .602 times 10 to the minus 19 kilograms.

03:47 Times the electric field, so 2 .5 times stands to the 4 newton per column, divided by the electron mass, which is 9 .109 times 10 to the minus 31 kilograms.

04:10 So this is going to give us an acceleration of 4 .4 times 10 to the 15 meters.

04:20 Per second squared...

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