### Example Problem 1: Coulomb’s Law in Two Dimensions**Given:**- **Sphere A:** Charge = +6.0 μC- **Sphere B:** Charge = -3.0 μC, located 4.0 cm to the right of Sphere A- **Sphere C:** Charge = +1.5 μC, located 3.0 cm directly beneath Sphere A**Analyze and Sketch the Problem:**1. **Establish Coordinate System:** Define +x and +y axes.2. **Sketch the Spheres:** - Place Sphere A at the origin. - Position Sphere B 4.0 cm to the right of Sphere A along the x-axis. - Position Sphere C 3.0 cm directly beneath Sphere A along the y-axis.3. **Label Distances and Forces:** - Distance \( r_{AB} \) between Sphere A and B: 4.0 cm - Distance \( r_{AC} \) between Sphere A and C: 3.0 cm - Represent force vectors \( F_{on\,A\,by\,B} \) and \( F_{on\,A\,by\,C} \)**Diagram:**``` y-axis ↑ | A (0,0) |\ | \rAC | \ | \ | C (0, -3.0 cm) | +------→ x-axis 4.0 cm B (4.0 cm, 0)```**Solve for the Unknown:**- Find the force of Sphere B on Sphere A- Find the force of Sphere C on Sphere A- Determine the net force on Sphere A \( F_{net\,A}\)### Steps:**1. Calculate Forces Using Coulomb’s Law:**The formula for Coulomb’s law is:\[ F = k \frac{|q_1 q_2|}{r^2} \]Where:- \( k = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2 \) (Coulomb's constant)- \( q_1 \text{ and } q_2 \) are the charges- \( r \) is the distance between the charges

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EXAMPLE Problem 1 Coulomb's Law in Two Dimensions Sphere A, with a charge of +6.0 μC, is located near another charged sphere, B. Sphere B has a charge of -3.0 μC and is located 4.0 cm to the right of A. a. What is the force of sphere B on sphere A? b. A third sphere, C, with a +1.5-μC charge, is added to the configuration. If it is located 3.0 cm directly beneath A, what is the new net force on sphere A? Analyze and Sketch the Problem . Establish coordinate axes and sketch the spheres. +y Show and label the distances between A B the spheres. . Diagram and label the force vectors. q8 Known: Unknown: 9A= +6.0 μC AB= 4.0 cm FB on A = ? = 98 -3.0 μC ГАС = 3.0 cm FC on A = ? 9c = +1.5 μC Fnet = ? 2 Solve for the Unknown a. Find the force of sphere B on sphere A. FB on A = K² AB TAB +x FAC TAB QA qc 109 Nm² FC on

EXAMPLE Problem 1 Coulomb's Law in Two Dimensions Sphere A, with a charge of +6.0 μC, is located near another charged sphere, B. Sphere B has a charge of -3.0 μC and is located 4.0 cm to the right of A. a. What is the force of sphere B on sphere A? b. A third sphere, C, with a +1.5-μC charge, is added to the configuration. If it is located 3.0 cm directly beneath A, what is the new net force on sphere A? Analyze and Sketch the Problem . Establish coordinate axes and sketch the spheres. +y Show and label the distances between A B the spheres. . Diagram and label the force vectors. q8 Known: Unknown: 9A= +6.0 μC AB= 4.0 cm FB on A = ? = 98 -3.0 μC ГАС = 3.0 cm FC on A = ? 9c = +1.5 μC Fnet = ? 2 Solve for the Unknown a. Find the force of sphere B on sphere A. FB on A = K² AB TAB +x FAC TAB QA qc 109 Nm² FC on

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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Review I ConstantS Periodic Table An electric dipole is formed from + 3.0 nC point charges spaced 3.0 mm apart. The dipole is centered at the origin, oriented along the y-axis. Part A What is the electric field strength at point (x, y) = ( 25 mm , 0 cm)? Express your answer using two significant figures. ΑΣφ ? E N/C Submit Request Answer Part B What is the electric field strength at point (x, y) = (0 cm, 25 mm ) ? Express your answer using two significant figures. ΑΣφ ? E N/C
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