# Electrons projected through an electron field problem

• glitterjewels
In summary, the problem involves electrons with an initial speed of 5 x 10^6 m/s being projected into a region with a constant electric field of 1 x 10^5 V/m, causing them to decelerate. The distance they travel before turning around can be found by solving the kinematic equation with final velocity set to 0 and initial velocity set to 5 x 10^6 m/s, and using the constant acceleration of qE/m.
glitterjewels

Here's the problem:
Electrons with initial speed of 5 x 10^6 m/s are projected into a region where a constant electric field of 1 x 10^5 V/m exists. The field is directed in a way that causes the electrons to DECELERATE. How far do the electrons travel before they turn around and move in the opposite direction?

My problem is I'm not sure how to find the distance or "how far". I may be missing an equation. Here's what I do have

F/m=acceleration=Fg=mg
The electric field=qE(volts/m)= 1 x 10^5 V/m
charge of electron qe= 1.06 x 10^-19c
acceleration upward= qE/m
Your help would be greatly appreciated! Thank you!

glitterjewels said:
Here's the problem:
Electrons with initial speed of 5 x 10^6 m/s are projected into a region where a constant electric field of 1 x 10^5 V/m exists. The field is directed in a way that causes the electrons to DECELERATE. How far do the electrons travel before they turn around and move in the opposite direction?

My problem is I'm not sure how to find the distance or "how far". I may be missing an equation. Here's what I do have

F/m=acceleration=Fg=mg
The electric field=qE(volts/m)= 1 x 10^5 V/m
charge of electron qe= 1.06 x 10^-19c
acceleration upward= qE/m
Your help would be greatly appreciated! Thank you!
Since motion direction isn't specified, it's presumed gravitational effects can be ignored. For these conditions, the following kinematic equation applies:

$$1: \ \ \ \ v_{final}^{2} \, - \, v_{initial}^{2} \, \ = \, \ 2 a d$$

where "v"s are the indicated velocities (here: vfinal=0, & vinitial=5e6 m/s), "d" the distance traveled, and "a" the constant acceleration (here: a=qE/m). Solve for "d".

~~

Last edited:

Sure, I'd be happy to help! Let's break down the problem and see what equations we can use to solve it.

First, we know that the electrons are projected with an initial speed of 5 x 10^6 m/s. This means that they have an initial kinetic energy, which we can calculate using the equation KE = 1/2 * mv^2.

Next, we know that the electrons are in a constant electric field of 1 x 10^5 V/m, which is causing them to decelerate. This means that the electrons are experiencing a force in the opposite direction of their motion, which we can calculate using the equation F = qE.

Now, we can use Newton's second law, F = ma, to relate the force to the acceleration. We know that the mass of an electron is 9.11 x 10^-31 kg, so we can plug in our values and solve for the acceleration (a = F/m).

Since we now have the acceleration, we can use the kinematic equation vf^2 = vi^2 + 2ad to find the final velocity (vf) of the electrons when they turn around. We know that the final velocity will be 0 m/s, since the electrons are turning around, so we can solve for the distance (d) that they travel before coming to a stop.

Therefore, the distance that the electrons travel before turning around is d = vf^2 / 2a. I hope this helps! Let me know if you have any further questions.

## 1. What is the purpose of projecting electrons through an electron field?

The purpose of projecting electrons through an electron field is to study the behavior and interactions of electrons in a controlled environment. This can help scientists understand the fundamental properties of electrons and their role in various physical processes.

## 2. How is an electron field created in this problem?

An electron field is created by applying an electric field to a region of space. This can be done using specialized equipment such as electron guns or particle accelerators. The strength and direction of the electric field can be controlled to manipulate the behavior of the electrons.

## 3. What factors affect the trajectory of electrons in this problem?

The trajectory of electrons in an electron field is influenced by several factors, including the strength and direction of the electric field, the initial velocity of the electrons, and any external forces acting on the electrons.

## 4. How is the behavior of electrons in an electron field related to real-world applications?

The study of electrons in an electron field has many practical applications, such as in the development of electronic devices like transistors and computers. Understanding the behavior of electrons also plays a crucial role in fields like particle physics, materials science, and engineering.

## 5. What are some challenges scientists face when studying electrons in an electron field?

One major challenge is the high precision and control required to manipulate and measure the behavior of individual electrons. Additionally, the behavior of electrons can be influenced by various external factors, making it challenging to isolate and study their behavior in a controlled environment.

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