College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

bartleby

Concept explainers

Question
**Electric Field and Potential Energy Calculation**

A uniform electric field of magnitude \(250 \, \text{V/m}\) is directed in the positive \(x\)-direction. A \(+10.0 \, \mu\text{C}\) charge moves from the origin to the point \((x, y) = (20.0 \, \text{cm}, 50.0 \, \text{cm})\).

**Questions:**

a) What is the change in the potential energy of the charge-field system?

b) Through what potential difference does the charge move?

---

**Explanation of the Problem:**

To solve these questions, we need to understand the relationship between electric fields, potential energy, and potential difference. The concepts involved include:

- The work done by the electric field,
- The potential difference between two points,
- The relationship between potential difference and change in potential energy.

Let's address each part separately with the relevant equations and concepts.

**Graph/Diagram Explanation (if any):**

There are no graphs or diagrams provided with this problem. The problem is described using the coordinates on a plane and indicating the direction of the electric field. 

**Key Formulas and Principles:**

1. The electric potential difference \(V\) is related to the electric field \(E\) by the equation \( V = E \cdot d \), where \(d\) is the distance moved in the direction of the field.

2. The change in potential energy \( \Delta U \) of a charge \( q \) moving through a potential difference \( V \) is given by \( \Delta U = q \cdot V \).

**Navigating the Solution:**

1. Look at the components of the movement: only the \( x \)-component affects the potential difference since the electric field is in the \( x \)-direction.
2. Calculate the \( x \)-component of the displacement.
3. Determine the potential difference.
4. Find the change in potential energy using the charge value and the calculated potential difference.

By carefully following these steps, one can determine both the potential energy change and the potential difference experienced by the charge.
expand button
Transcribed Image Text:**Electric Field and Potential Energy Calculation** A uniform electric field of magnitude \(250 \, \text{V/m}\) is directed in the positive \(x\)-direction. A \(+10.0 \, \mu\text{C}\) charge moves from the origin to the point \((x, y) = (20.0 \, \text{cm}, 50.0 \, \text{cm})\). **Questions:** a) What is the change in the potential energy of the charge-field system? b) Through what potential difference does the charge move? --- **Explanation of the Problem:** To solve these questions, we need to understand the relationship between electric fields, potential energy, and potential difference. The concepts involved include: - The work done by the electric field, - The potential difference between two points, - The relationship between potential difference and change in potential energy. Let's address each part separately with the relevant equations and concepts. **Graph/Diagram Explanation (if any):** There are no graphs or diagrams provided with this problem. The problem is described using the coordinates on a plane and indicating the direction of the electric field. **Key Formulas and Principles:** 1. The electric potential difference \(V\) is related to the electric field \(E\) by the equation \( V = E \cdot d \), where \(d\) is the distance moved in the direction of the field. 2. The change in potential energy \( \Delta U \) of a charge \( q \) moving through a potential difference \( V \) is given by \( \Delta U = q \cdot V \). **Navigating the Solution:** 1. Look at the components of the movement: only the \( x \)-component affects the potential difference since the electric field is in the \( x \)-direction. 2. Calculate the \( x \)-component of the displacement. 3. Determine the potential difference. 4. Find the change in potential energy using the charge value and the calculated potential difference. By carefully following these steps, one can determine both the potential energy change and the potential difference experienced by the charge.
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Physics
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
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON