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In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053 nm around a stationary proton. How many revolutions per second does the electron make?
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Ch 22: Electric Charges and Forces
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 22, Problema 49b
A +2.0 nC charge is at the origin and a −4.0 nC charge is at x = 1.0 cm. Would the net force be zero for an electron placed at the same position? Explain.
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Step 1: Begin by recalling Coulomb's Law, which describes the force between two charges. The formula is: , where is Coulomb's constant, and are the charges, and is the distance between them.
Step 2: Consider the electron placed at the same position as the −4.0 nC charge (x = 1.0 cm). The electron will experience forces due to both the +2.0 nC charge at the origin and the −4.0 nC charge at x = 1.0 cm.
Step 3: Analyze the direction of the forces. The electron has a negative charge, so it will be attracted to the positive +2.0 nC charge at the origin and repelled by the negative −4.0 nC charge at x = 1.0 cm. These forces act in opposite directions along the x-axis.
Step 4: Calculate the magnitudes of the forces using Coulomb's Law for each interaction. For the force due to the +2.0 nC charge, use the distance of 1.0 cm (converted to meters). For the force due to the −4.0 nC charge, the distance is effectively zero since the electron is at the same position as the −4.0 nC charge.
Step 5: Conclude that the net force cannot be zero because the force due to the −4.0 nC charge is undefined at zero distance (it approaches infinity), and the force due to the +2.0 nC charge is finite. Therefore, the electron would experience a net force and the system would not be in equilibrium.
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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 law is fundamental for calculating the forces acting on charges in an electric field.
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Percorso guidato
09:52
Coulomb's Law
Superposition Principle
The Superposition Principle in electrostatics states that the total force acting on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge. This principle allows us to analyze complex charge configurations by considering the effect of each charge separately before combining the results.
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03:32Superposition of Sinusoidal Wave Functions
Electric Field
An electric field is a region around a charged object where other charges experience a force. The strength and direction of the electric field depend on the source charge and its position. For an electron placed in an electric field, the force it experiences will depend on the field's direction and magnitude, which can help determine if the net force on it is zero.
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Percorso guidato
03:16Intro to Electric Fields
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