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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![**Problem Statement:**
Three charges on the xy plane are \( Q_1 = +3.00 \, \mu C \), \( Q_2 = +2.00 \, \mu C \), and \( Q_3 = +3.00 \, \mu C \). Suppose the coordinates for \( Q_1 \) are (0.250 m, 0.00 m), while for \( Q_3 \) the coordinates are (0.00 m, 0.250 m). Finally, suppose \( Q_2 \) is located at the origin, (0.00 m, 0.00 m). In the questions below, vector-valued forces may be stated as ordered pairs.
**a. Sketch the Charge Configuration:**
The diagram shows a triangle formed by the charges \( Q_1 \), \( Q_2 \), and \( Q_3 \) on the xy plane. The coordinates for each charge are:
- \( Q_1 \) at (0.250 m, 0.00 m)
- \( Q_2 \) at the origin (0.00 m, 0.00 m)
- \( Q_3 \) at (0.00 m, 0.250 m)
The distance \( c \) between \( Q_1 \) and \( Q_3 \) is calculated using the Pythagorean theorem and is approximately 0.35 m.
**b. Calculate the Vector-Valued Electrostatic Force on \( Q_2 \) due to \( Q_1 \):**
Using Coulomb’s Law:
\[ F = \frac{k \cdot Q_2 \cdot Q_1}{R^2} \]
\[ F = \frac{k \cdot (3 \times 10^{-6})}{(0.25)^2} \]
The calculation results are shown as \( 4.32 \times 10^5 \).
**c. Calculate the Vector-Valued Electrostatic Force on \( Q_2 \) due to \( Q_3 \):**
Using Coulomb’s Law:
\[ F = \frac{k \cdot Q_2 \cdot Q_3}{R^2} \]
\[ F = \frac{k \cdot (3 \times 10^{-6})}{(0.25)^2} = 4.1 \]
**d. Calculate the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa442f039-c23f-4767-9723-571e7d7e1a22%2F12d28b2e-16d8-4709-97e9-a3d67259b868%2F0zea7u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Three charges on the xy plane are \( Q_1 = +3.00 \, \mu C \), \( Q_2 = +2.00 \, \mu C \), and \( Q_3 = +3.00 \, \mu C \). Suppose the coordinates for \( Q_1 \) are (0.250 m, 0.00 m), while for \( Q_3 \) the coordinates are (0.00 m, 0.250 m). Finally, suppose \( Q_2 \) is located at the origin, (0.00 m, 0.00 m). In the questions below, vector-valued forces may be stated as ordered pairs.
**a. Sketch the Charge Configuration:**
The diagram shows a triangle formed by the charges \( Q_1 \), \( Q_2 \), and \( Q_3 \) on the xy plane. The coordinates for each charge are:
- \( Q_1 \) at (0.250 m, 0.00 m)
- \( Q_2 \) at the origin (0.00 m, 0.00 m)
- \( Q_3 \) at (0.00 m, 0.250 m)
The distance \( c \) between \( Q_1 \) and \( Q_3 \) is calculated using the Pythagorean theorem and is approximately 0.35 m.
**b. Calculate the Vector-Valued Electrostatic Force on \( Q_2 \) due to \( Q_1 \):**
Using Coulomb’s Law:
\[ F = \frac{k \cdot Q_2 \cdot Q_1}{R^2} \]
\[ F = \frac{k \cdot (3 \times 10^{-6})}{(0.25)^2} \]
The calculation results are shown as \( 4.32 \times 10^5 \).
**c. Calculate the Vector-Valued Electrostatic Force on \( Q_2 \) due to \( Q_3 \):**
Using Coulomb’s Law:
\[ F = \frac{k \cdot Q_2 \cdot Q_3}{R^2} \]
\[ F = \frac{k \cdot (3 \times 10^{-6})}{(0.25)^2} = 4.1 \]
**d. Calculate the
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