Textbook Question
A −10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. What is the electric potential at the point on the x-axis where the electric field is zero?
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Ch 25: The Electric Potential
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 25, Problem 40b
Two small metal cubes with masses 2.0 g and 4.0 g are tied together by a 5.0-cm-long massless string and are at rest on a frictionless surface. Each is charged to +2.0 μC. What is the tension in the string?
Verified step by step guidance1
Convert the given masses of the cubes from grams to kilograms. Since 1 g = 0.001 kg, the masses are m₁ = 0.002 kg and m₂ = 0.004 kg.
Calculate the electrostatic force between the two charged cubes using Coulomb's law: F = (k * |q₁ * q₂|) / r², where k = 8.99 × 10⁹ N·m²/C² (Coulomb's constant), q₁ = q₂ = 2.0 × 10⁻⁶ C, and r = 0.05 m (the length of the string).
Substitute the values into Coulomb's law formula to find the magnitude of the electrostatic force: F = (8.99 × 10⁹ * (2.0 × 10⁻⁶)²) / (0.05)².
Recognize that the tension in the string must balance the electrostatic force because the system is in equilibrium (the cubes are at rest). Therefore, the tension in the string is equal to the magnitude of the electrostatic force.
State that the tension in the string is numerically equal to the calculated electrostatic force, which can be determined by completing the substitution and performing the arithmetic.
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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 is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This principle is essential for calculating the force acting on the cubes due to their charges.
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09:52
Coulomb's Law
Newton's Second Law
Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law is crucial for determining the relationship between the forces acting on the cubes and the resulting tension in the string, as it allows us to analyze the motion of the system.
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Tension in a String
Tension is the force transmitted through a string or rope when it is pulled tight by forces acting at either end. In this scenario, the tension in the string connecting the two charged cubes must balance the electrostatic force between them, allowing us to calculate the tension based on the forces involved and the masses of the cubes.
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Related Practice
Textbook Question
A proton's speed as it passes point 1 is 50,000 m/s. It follows the trajectory shown in FIGURE P25.43. What is the proton's speed at point 2?
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Textbook Question
A +3.0 nC charge is at x=0 cm and a −1.0 nC charge is at x=4 cm. At what point or points on the x-axis is the electric potential zero?
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Textbook Question
A −3.0 nC charge is on the x-axis at x=−9 cm and a +4.0 nC charge is on the x-axis at x=16 cm. At what point or points on the y-axis is the electric potential zero?
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Textbook Question
Two point charges 2.0 cm apart have an electric potential energy −180 μJ. The total charge is 30 nC. What are the two charges?
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Textbook Question
The four 1.0 g spheres shown in FIGURE P25.42 are released simultaneously and allowed to move away from each other. What is the speed of each sphere when they are very far apart?
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