**Problem Statement:**Three charged metal spheres, \( q1 = -5.42 \, \text{nC} \), \( q2 = 3.08 \, \text{nC} \), and \( q3 = -2.56 \, \text{nC} \), are arrayed in the xy-plane so that they form an equilateral triangle with \( d = 12.0 \, \text{cm} \), as shown in the figure.**Question:**What is the net electrostatic force on the sphere at the origin?**Solution Format:**\[ \mathbf{F} = \left( \_\_\_\_ \, \text{N} \right) \mathbf{\hat{i}} - \left( \_\_\_\_ \, \text{N} \right) \mathbf{\hat{j}} \]**Diagram Explanation:**- **Graph Description:** The diagram is a two-dimensional graph depicting the positional arrangement of three charged spheres. The spheres are positioned so that they form an equilateral triangle. - **Axes:** - The vertical axis is labeled 'y'. - The horizontal axis is labeled 'x'. - **Sphere Positions:** - Sphere \( q1 \) is located at the origin of the graph. - Sphere \( q2 \) is positioned along the positive x-axis at a distance of 12.0 cm from \( q1 \). - Sphere \( q3 \) is located above and to the left of \( q1 \) and \( q2 \), forming a 60° angle with both axes. **Diagram Key Points:**- The sides of the triangle formed by the charges are all equal (12.0 cm).- An angle of 60° is formed between each of the sides in the equilateral triangle. This problem involves calculating the net electrostatic force experienced by one of the charges at the origin due to the other two charges. The forces between the charges can be resolved into components along the x and y axes, and then summed vectorially to find the total force.

Given : q1= -5.42 nC= -5.42×10-9 Cq2= 3.08 nC= 3.08×10-9 Cq1= -2.56 nC= -2.56×10-9 CSide length of…

Three charged metal spheres, 9₁ = -5.42 nC, 92= 3.08 nC, and q3 = -2.56 nC, are arrayed in the xy plane so that they form an equilateral triangle with d= 12.0 cm, as shown in the figure. What is the net electrostatic force on the sphere at the origin? 7 = N)Ĵ 93 12.0 cm 92 91 60°

Three charged metal spheres, 9₁ = -5.42 nC, 92= 3.08 nC, and q3 = -2.56 nC, are arrayed in the xy plane so that they form an equilateral triangle with d= 12.0 cm, as shown in the figure. What is the net electrostatic force on the sphere at the origin? 7 = N)Ĵ 93 12.0 cm 92 91 60°

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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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

**Problem Statement:**

Three charged metal spheres, \( q1 = -5.42 \, \text{nC} \), \( q2 = 3.08 \, \text{nC} \), and \( q3 = -2.56 \, \text{nC} \), are arrayed in the xy-plane so that they form an equilateral triangle with \( d = 12.0 \, \text{cm} \), as shown in the figure.

**Question:**
What is the net electrostatic force on the sphere at the origin?

**Solution Format:**
\[ \mathbf{F} = \left( \_\_\_\_ \, \text{N} \right) \mathbf{\hat{i}} - \left( \_\_\_\_ \, \text{N} \right) \mathbf{\hat{j}} \]

**Diagram Explanation:**

- **Graph Description:**
The diagram is a two-dimensional graph depicting the positional arrangement of three charged spheres. The spheres are positioned so that they form an equilateral triangle.

- **Axes:**
- The vertical axis is labeled 'y'.
- The horizontal axis is labeled 'x'.

- **Sphere Positions:**
- Sphere \( q1 \) is located at the origin of the graph.
- Sphere \( q2 \) is positioned along the positive x-axis at a distance of 12.0 cm from \( q1 \).
- Sphere \( q3 \) is located above and to the left of \( q1 \) and \( q2 \), forming a 60° angle with both axes.

**Diagram Key Points:**

- The sides of the triangle formed by the charges are all equal (12.0 cm).
- An angle of 60° is formed between each of the sides in the equilateral triangle.

This problem involves calculating the net electrostatic force experienced by one of the charges at the origin due to the other two charges. The forces between the charges can be resolved into components along the x and y axes, and then summed vectorially to find the total force.

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