Textbook Question
What are the strength and direction of the electric field 1.0 mm from a proton?
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 20
What is the force F on the 1.0 nC charge in FIGURE EX22.20? Give your answer as a magnitude and a direction.
Verified step by step guidance1
Identify the charges and their positions in FIGURE EX22.20. Note the charge values, their distances, and the configuration of the system. The 1.0 nC charge is the one experiencing the net force due to the other charges.
Use Coulomb's Law to calculate the force between the 1.0 nC charge and each of the other charges. Coulomb's Law is given by: , where is the Coulomb constant, and are the charges, and is the distance between them.
Determine the direction of each force vector. Remember that like charges repel and opposite charges attract. Use the geometry of the system to resolve the forces into their components along the x-axis and y-axis, if necessary.
Add the force vectors to find the net force on the 1.0 nC charge. Use vector addition: . Combine the x and y components using the Pythagorean theorem to find the magnitude of the net force: .
Determine the direction of the net force using trigonometry. The angle can be found using . Express the final answer as a magnitude and direction.
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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 force (F) is directly proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The formula is F = k * (|q1 * q2|) / r², where k is Coulomb's constant. This law is fundamental for calculating the force on a charge due to other charges.
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Coulomb's Law
Electric Field
An electric field (E) is a region around a charged object where other charges experience a force. It is defined as the force per unit charge experienced by a positive test charge placed in the field, given by E = F/q. The direction of the electric field is away from positive charges and towards negative charges. Understanding electric fields is crucial for determining the force on a charge in a given configuration.
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Vector Addition
Vector addition is the process of combining two or more vectors to determine a resultant vector. In physics, forces are vectors that have both magnitude and direction. When multiple forces act on a charge, the net force is found by adding the individual force vectors, taking into account their directions. This concept is essential for accurately determining the total force acting on the charge in the problem.
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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
What is the magnitude of the net force on charge A in FIGURE EX22.17?
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?