20. (II) A +35 µC point charge is placed 46 cm from an identi- cal +35 µC charge. How much work would be required to move a +0.50 μC test charge from a point midway between them to a point 12 cm closer to either of the charges?
20. (II) A +35 µC point charge is placed 46 cm from an identi- cal +35 µC charge. How much work would be required to move a +0.50 μC test charge from a point midway between them to a point 12 cm closer to either of the charges?
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)...
Related questions
Question
100%
please type your solution so that it is easy for to read I have bad eyesight please and thank you
![### Problem Statement
**Question 20:**
A +35 µC point charge is placed 46 cm from an identical +35 µC charge. How much work would be required to move a +0.50 µC test charge from a point midway between them to a point 12 cm closer to either of the charges?
### Explanation
This is a physics problem involving electrostatics, specifically the calculation of work required to move a test charge in the presence of other point charges. Let's break down the information provided:
1. **Initial Setup:**
- There are two point charges, each of +35 µC (microcoulombs), placed 46 cm apart.
- A +0.50 µC test charge is initially placed at the midpoint between these two charges.
2. **Objective:**
- To calculate the work required to move the +0.50 µC test charge to a point that is 12 cm closer to either of the +35 µC charges.
### Detailed Information:
1. **Initial Distance:**
- The midpoint between the charges is 23 cm from each +35 µC charge (since 46 cm / 2 = 23 cm).
2. **Final Distance:**
- After moving the test charge 12 cm closer to one of the charges, the new distance will be (23 cm - 12 cm) = 11 cm from that charge.
- It will be (23 cm + 12 cm) = 35 cm from the other +35 µC charge.
### Charge Interaction and Formulas:
- The work \( W \) required to move a charge \( q \) in the presence of other charges is given by:
\[
W = q \Delta V
\]
where \( \Delta V \) is the change in electric potential.
- The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is:
\[
V = \frac{kQ}{r}
\]
where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).
### Initial and Final Potential:
- **Initial Potential at Midpoint:**
\[
V_\text{initial} = \frac{k \cdot 35 \times 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa96c07fd-e70d-478a-a514-a2ec6704d773%2F524df61c-dc86-4bd7-b686-fa9fa902ef9f%2Foypx45ha_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Question 20:**
A +35 µC point charge is placed 46 cm from an identical +35 µC charge. How much work would be required to move a +0.50 µC test charge from a point midway between them to a point 12 cm closer to either of the charges?
### Explanation
This is a physics problem involving electrostatics, specifically the calculation of work required to move a test charge in the presence of other point charges. Let's break down the information provided:
1. **Initial Setup:**
- There are two point charges, each of +35 µC (microcoulombs), placed 46 cm apart.
- A +0.50 µC test charge is initially placed at the midpoint between these two charges.
2. **Objective:**
- To calculate the work required to move the +0.50 µC test charge to a point that is 12 cm closer to either of the +35 µC charges.
### Detailed Information:
1. **Initial Distance:**
- The midpoint between the charges is 23 cm from each +35 µC charge (since 46 cm / 2 = 23 cm).
2. **Final Distance:**
- After moving the test charge 12 cm closer to one of the charges, the new distance will be (23 cm - 12 cm) = 11 cm from that charge.
- It will be (23 cm + 12 cm) = 35 cm from the other +35 µC charge.
### Charge Interaction and Formulas:
- The work \( W \) required to move a charge \( q \) in the presence of other charges is given by:
\[
W = q \Delta V
\]
where \( \Delta V \) is the change in electric potential.
- The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is:
\[
V = \frac{kQ}{r}
\]
where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).
### Initial and Final Potential:
- **Initial Potential at Midpoint:**
\[
V_\text{initial} = \frac{k \cdot 35 \times 10
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
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…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON