Textbook Question
What is the force F on the 1.0 nC charge in FIGURE EX22.20? Give your answer as a magnitude and a direction.
Ch 22: Electric Charges and Forces
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 22, Problem 17
What is the magnitude of the net force on charge A in FIGURE EX22.17?
Verified step by step guidance1
Step 1: Identify the charges involved in the problem and their positions relative to charge A. Use the diagram in FIGURE EX22.17 to determine the distances between charge A and the other charges.
Step 2: Recall Coulomb's Law, which states that the force between two charges is given by \( F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \), where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them.
Step 3: Calculate the individual forces exerted on charge A by the other charges using Coulomb's Law. Ensure you account for the direction of each force (attractive or repulsive) based on the signs of the charges.
Step 4: Break the forces into their components (e.g., \( F_x \) and \( F_y \)) if the forces are not aligned along the same axis. Use trigonometric functions such as sine and cosine to resolve the forces into components.
Step 5: Sum the components of the forces to find the net force on charge A. Use the Pythagorean theorem \( F_{net} = \sqrt{F_x^2 + F_y^2} \) to calculate the magnitude of the net force.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Coulomb's Law
Coulomb's Law describes the electrostatic force between two charged objects. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental for calculating the forces acting on charged particles in an electric field.
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Coulomb's Law
Net Force
The net force is the vector sum of all individual forces acting on an object. In the context of charged particles, it involves considering both the magnitudes and directions of forces due to other charges. Understanding how to calculate the net force is crucial for determining the overall effect on a charge, such as charge A in the given scenario.
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Vector Addition
Vector addition is the process of combining vectors to determine a resultant vector. In physics, forces are represented as vectors, which have both magnitude and direction. To find the net force on charge A, one must add the forces from other charges as vectors, taking into account their directions to accurately compute the total force acting on charge A.
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Related Practice
Textbook Question
A massless spring is attached to a support at one end and has a 2.0 μC charge glued to the other end. A −4.0 μC charge is slowly brought near. The spring has stretched 1.2 cm when the charges are 2.6 cm apart. What is the spring constant of the spring?
Textbook Question
Two protons are 2.0 fm apart. What is the magnitude of the gravitational force on one proton due to the other proton?
Textbook Question
Figure 22.8 showed how an electroscope becomes negatively charged. The leaves will also repel each other if you touch the electroscope with a positively charged glass rod. Use a series of charge diagrams to explain what happens and why the leaves repel each other.
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Textbook Question
A 2.0 g plastic bead charged to −4.0 nC and a 4.0 g glass bead charged to +8.0 nC are 2.0 cm apart and free to move. What are the accelerations of the plastic bead?
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Textbook Question
Two small plastic spheres each have a mass of 2.0 g and a charge of −50.0 nC. They are placed 2.0 cm apart (center to center). What is the magnitude of the electric force on each sphere?