Domanda del libro di testo
Two spherical drops of mercury each have a charge of 0.10 nC and a potential of 300 V at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?
132
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 68
Two metal objects that are in contact must be at the same potential, an assertion we'll prove in the next chapter. Suppose a metal sphere of radius R is charged to 1000 V and a second metal sphere of radius 2R is charged to 2000 V. The two spheres are brought into contact and then separated. Afterward, what is the potential of each sphere?
Guida verificata passo dopo passo1
Step 1: Understand the concept of charge redistribution. When two conductors are brought into contact, charge redistributes between them until they reach the same electric potential. This is because charges move to minimize potential differences.
Step 2: Write the formula for the potential of a sphere. The potential of a charged sphere is given by \( V = \frac{Q}{4 \pi \epsilon_0 R} \), where \( Q \) is the charge, \( R \) is the radius, and \( \epsilon_0 \) is the permittivity of free space.
Step 3: Use the principle of charge conservation. The total charge before contact is equal to the total charge after contact. Let \( Q_1 \) and \( Q_2 \) be the initial charges on the spheres, and \( Q_1' \) and \( Q_2' \) be the charges after contact. Then, \( Q_1 + Q_2 = Q_1' + Q_2' \).
Step 4: Set the potentials equal after contact. Since the spheres are in contact, their potentials become equal: \( \frac{Q_1'}{4 \pi \epsilon_0 R} = \frac{Q_2'}{4 \pi \epsilon_0 (2R)} \). Simplify this equation to relate \( Q_1' \) and \( Q_2' \).
Step 5: Solve for the final potential. Use the charge conservation equation and the relationship between \( Q_1' \) and \( Q_2' \) to find the total charge and distribute it between the spheres. Substitute the charges into the potential formula to find the final potential of each sphere.
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, measured in volts (V), is the amount of electric potential energy per unit charge at a point in an electric field. It indicates how much work would be done to move a charge from a reference point to a specific point within the field. In this scenario, the potentials of the two spheres before contact are crucial for understanding how they will equalize when brought into contact.
Video consigliato:
Percorso guidato
07:33
Electric Potential
Charge Distribution
When two conductive objects come into contact, charge redistributes between them until they reach the same electric potential. The total charge is conserved, meaning the sum of the charges on both spheres before contact equals the sum after they are separated. This principle is essential for determining the final potential of each sphere after they are disconnected.
Video consigliato:
Percorso guidato
04:03Probability Distribution Graph
Capacitance
Capacitance is the ability of a system to store charge per unit potential difference and is influenced by the geometry of the conductors. For spheres, capacitance is proportional to their radius, meaning a larger sphere can hold more charge at the same potential. Understanding capacitance helps in calculating how the charges will distribute between the two spheres based on their sizes and initial potentials.
Video consigliato:
Percorso guidato
08:02Capacitors & Capacitance (Intro)
Pratica correlata
Domanda del libro di testo
FIGURE P25.72 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center.
442
views
Domanda del libro di testo
FIGURE P25.67 shows two uniformly charged spheres. What is the potential difference between points 1 and 2? Which point is at the higher potential? Hint: The potential at any point is the superposition of the potentials due to all charges.
172
views
Domanda del libro di testo
FIGURE P25.70 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.
307
views
Domanda del libro di testo
The wire in FIGURE P25.74 has linear charge density λ. What is the electric potential at the center of the semicircle?
182
views
Domanda del libro di testo
A Van de Graaff generator is a device for generating a large electric potential by building up charge on a hollow metal sphere. A typical classroom-demonstration model has a diameter of 30 cm. What is the electric field strength just outside the surface of the sphere when it is charged to 500,000 V?
1699
views