Domanda del libro di testo
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?
63
views
Ch 25: The Electric Potential
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 25, Problema 39
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?
Guida verificata passo dopo passo1
Understand the problem: The electric potential at a point due to a charge is given by the formula \( V = \frac{kq}{r} \), where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge to the point. The goal is to find the point(s) on the x-axis where the total electric potential from both charges is zero.
Set up the equation for the total electric potential: The total potential at a point \( x \) on the x-axis is the sum of the potentials due to the two charges. Let the distance from the +3.0 nC charge to the point be \( r_1 \) and the distance from the −1.0 nC charge to the point be \( r_2 \). The equation becomes \( \frac{k(3.0 \times 10^{-9})}{r_1} + \frac{k(-1.0 \times 10^{-9})}{r_2} = 0 \).
Express the distances \( r_1 \) and \( r_2 \) in terms of \( x \): Since the +3.0 nC charge is at \( x = 0 \) cm and the −1.0 nC charge is at \( x = 4 \) cm, \( r_1 = |x| \) and \( r_2 = |x - 4| \). Substitute these into the equation: \( \frac{k(3.0 \times 10^{-9})}{|x|} + \frac{k(-1.0 \times 10^{-9})}{|x - 4|} = 0 \).
Simplify the equation: Cancel out \( k \) (since it is a common factor) and rewrite the equation as \( \frac{3.0 \times 10^{-9}}{|x|} = \frac{1.0 \times 10^{-9}}{|x - 4|} \). Simplify further to \( \frac{3}{|x|} = \frac{1}{|x - 4|} \).
Solve for \( x \): Cross-multiply to get \( 3|x - 4| = |x| \). This equation can be solved by considering the different cases for \( x \) (e.g., \( x < 0 \), \( 0 < x < 4 \), and \( x > 4 \)) to find the point(s) where the electric potential is zero. Analyze each case to determine the valid solution(s).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Electric Potential
Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It is a scalar quantity measured in volts (V) and indicates the work done to move a unit positive charge from a reference point to a specific point in the field without any acceleration.
Video consigliato:
Percorso guidato
07:33
Electric Potential
Superposition Principle
The superposition principle states that the total electric potential at a point due to multiple charges is the algebraic sum of the potentials due to each charge individually. This principle allows us to analyze complex charge configurations by considering the contributions from each charge separately.
Video consigliato:
Percorso guidato
03:32Superposition of Sinusoidal Wave Functions
Distance and Charge Relationship
The electric potential created by a point charge decreases with distance from the charge. Specifically, the potential (V) due to a point charge (Q) at a distance (r) is given by V = kQ/r, where k is Coulomb's constant. This relationship is crucial for determining where the total potential is zero, as it helps identify the influence of each charge at various points along the x-axis.
Video consigliato:
Percorso guidato
07:12Distance to Stop a Point Charge
Pratica correlata
Domanda del libro di testo
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?
2524
views
1
rank
Domanda del libro di testo
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?
1911
views
Domanda del libro di testo
Two point charges qₐ and qᵦ are located on the x-axis at x=a and x=b. FIGURE EX25.36 is a graph of V, the electric potential. Draw a graph of Eₓ, the x-component of the electric field, as a function of x.
1996
views
Domanda del libro di testo
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?
167
views
Domanda del libro di testo
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?
2586
views
1
rank