Homework Help is Here – Start Your Trial Now!
Science
Physics
An electron is initially at rest at distance 0.15 m from a fixed charge Q = -5.00×10-9 C. The electron accelerates. How fast is it moving when the distance is 0.3 m?

An electron is initially at rest at distance 0.15 m from a fixed charge Q = -5.00×10-9 C. The electron accelerates. How fast is it moving when the distance is 0.3 m?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question
**Problem Statement:** An electron is initially at rest at a distance of 0.15 m from a fixed charge \( Q = -5.00 \times 10^{-9} \) C. The electron accelerates. How fast is it moving when the distance is 0.3 m? --- **Explanation:** To solve this problem, you'll need to use principles of electrostatic force and energy conservation. Here’s a step-by-step guide: 1. **Coulomb’s Law:** Calculate the electrostatic force between the charge \( Q \) and the electron at the initial and final positions. 2. **Electric Potential Energy:** Determine the initial and final electric potential energy of the electron by the formula: \[ U = \frac{k \cdot Q \cdot q}{r} \] where: - \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)), - \( q \) is the charge of the electron (\(-1.60 \times 10^{-19} \, \text{C}\)), - \( r \) is the distance from the charge. 3. **Conservation of Energy:** Apply the conservation of energy principle. The loss in electric potential energy converts into kinetic energy of the electron: \[ \Delta U = - \Delta K \] 4. **Kinetic Energy:** Calculate the change in kinetic energy to find the speed \( v \) of the electron: \[ K = \frac{1}{2} mv^2 \] where \( m \) is the mass of the electron (\(9.11 \times 10^{-31} \, \text{kg}\)). 5. **Equation Solving:** Solve for \( v \) using the conservation equation: \[ \Delta U = \frac{1}{2} mv^2 \] This solution approach combines physics concepts to find out how fast the electron is moving at a new distance.
Transcribed Image Text:**Problem Statement:** An electron is initially at rest at a distance of 0.15 m from a fixed charge \( Q = -5.00 \times 10^{-9} \) C. The electron accelerates. How fast is it moving when the distance is 0.3 m? --- **Explanation:** To solve this problem, you'll need to use principles of electrostatic force and energy conservation. Here’s a step-by-step guide: 1. **Coulomb’s Law:** Calculate the electrostatic force between the charge \( Q \) and the electron at the initial and final positions. 2. **Electric Potential Energy:** Determine the initial and final electric potential energy of the electron by the formula: \[ U = \frac{k \cdot Q \cdot q}{r} \] where: - \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)), - \( q \) is the charge of the electron (\(-1.60 \times 10^{-19} \, \text{C}\)), - \( r \) is the distance from the charge. 3. **Conservation of Energy:** Apply the conservation of energy principle. The loss in electric potential energy converts into kinetic energy of the electron: \[ \Delta U = - \Delta K \] 4. **Kinetic Energy:** Calculate the change in kinetic energy to find the speed \( v \) of the electron: \[ K = \frac{1}{2} mv^2 \] where \( m \) is the mass of the electron (\(9.11 \times 10^{-31} \, \text{kg}\)). 5. **Equation Solving:** Solve for \( v \) using the conservation equation: \[ \Delta U = \frac{1}{2} mv^2 \] This solution approach combines physics concepts to find out how fast the electron is moving at a new distance.
Expert Solution
Step 1: Change in potential and kinetic energy

The initial potential energy will be converted into kinetic energy:

Where,

U subscript 1 is initial potential energy,

U subscript 2 is final potential energy,

K subscript 1 is initial kinetic energy,

K subscript 2 is final potential energy,


steps

Step by step

Solved in 3 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Electric field
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS