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)...
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![### Understanding Forces Between Point Charges
In the image, we are examining the forces between three point charges and how they affect a fourth charge placed at point A. The given point charges are:
- \( Q_1 = 15.4 \, \mu \text{C} \)
- \( Q_2 = -30.6 \, \mu \text{C} \)
- \( Q_3 = 87.3 \, \mu \text{C} \)
These charges are arranged in a square configuration. Additionally, a fourth point charge at point A has a charge \( Q_A = 13.5 \, \mu \text{C} \).
### Diagram Analysis
The diagram depicts the spatial arrangement of the charges as follows:
- \( Q_1 \) and \( Q_2 \) are aligned vertically along the left side of the square.
- \( Q_3 \) is positioned on the bottom right of the square.
- Point A, where charge \( Q_A \) is located, is at the top right corner of the square.
The square formed by these charges has equal sides \( x \) and \( y \), both measuring \( 70.1 \) cm (which is 0.701 m).
### Objective
The goal is to calculate the magnitude \( F \) of the net force exerted on the charge at point A, \( Q_A \), due to the other three point charges \( Q_1, Q_2, \) and \( Q_3 \).
\[ F = \, \boxed{\hspace{7cm}} \, \text{N} \]
### Steps for Calculation:
1. **Convert All Charges to Coulombs:**
- \( Q_1 = 15.4 \times 10^{-6} \, \text{C} \)
- \( Q_2 = -30.6 \times 10^{-6} \, \text{C} \)
- \( Q_3 = 87.3 \times 10^{-6} \, \text{C} \)
- \( Q_A = 13.5 \times 10^{-6} \, \text{C} \)
2. **Use Coulomb’s Law:**
Coulomb's law states that the force between any two point charges is given by:
\[
F = k_e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e1db01-06d0-4e20-aae1-26f96b6814c3%2Ff3b8dc07-6ac3-4bf0-beab-f08aad758454%2Ffcfhk3b_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Forces Between Point Charges
In the image, we are examining the forces between three point charges and how they affect a fourth charge placed at point A. The given point charges are:
- \( Q_1 = 15.4 \, \mu \text{C} \)
- \( Q_2 = -30.6 \, \mu \text{C} \)
- \( Q_3 = 87.3 \, \mu \text{C} \)
These charges are arranged in a square configuration. Additionally, a fourth point charge at point A has a charge \( Q_A = 13.5 \, \mu \text{C} \).
### Diagram Analysis
The diagram depicts the spatial arrangement of the charges as follows:
- \( Q_1 \) and \( Q_2 \) are aligned vertically along the left side of the square.
- \( Q_3 \) is positioned on the bottom right of the square.
- Point A, where charge \( Q_A \) is located, is at the top right corner of the square.
The square formed by these charges has equal sides \( x \) and \( y \), both measuring \( 70.1 \) cm (which is 0.701 m).
### Objective
The goal is to calculate the magnitude \( F \) of the net force exerted on the charge at point A, \( Q_A \), due to the other three point charges \( Q_1, Q_2, \) and \( Q_3 \).
\[ F = \, \boxed{\hspace{7cm}} \, \text{N} \]
### Steps for Calculation:
1. **Convert All Charges to Coulombs:**
- \( Q_1 = 15.4 \times 10^{-6} \, \text{C} \)
- \( Q_2 = -30.6 \times 10^{-6} \, \text{C} \)
- \( Q_3 = 87.3 \times 10^{-6} \, \text{C} \)
- \( Q_A = 13.5 \times 10^{-6} \, \text{C} \)
2. **Use Coulomb’s Law:**
Coulomb's law states that the force between any two point charges is given by:
\[
F = k_e
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