Textbook Question
Two small charged spheres are 5.0 cm apart. One is charged to +25 nC, the other to −15 nC. A proton is released from rest halfway between the spheres. What is the proton's speed after it has moved 1.0 cm?
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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 36b
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. What is the ratio |qₐ/qᵦ|?
Verified step by step guidance1
Step 1: Understand the relationship between electric potential (V) and point charges. The electric potential due to a point charge q at a distance r is given by V = k * q / r, where k is Coulomb's constant.
Step 2: Analyze the graph provided. The graph shows two peaks at x = a and x = b, corresponding to the locations of the charges qₐ and qᵦ. The height of each peak represents the magnitude of the electric potential at those points.
Step 3: Note that the electric potential is proportional to the magnitude of the charge. The ratio of the heights of the peaks on the graph corresponds to the ratio of the magnitudes of the charges |qₐ| and |qᵦ|.
Step 4: Measure or compare the heights of the peaks at x = a and x = b from the graph. Let the height of the peak at x = a be Vₐ and the height of the peak at x = b be Vᵦ.
Step 5: Calculate the ratio |qₐ/qᵦ| using the proportionality between the electric potential and the charge. The ratio is given by |qₐ/qᵦ| = Vₐ / Vᵦ.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electric Potential (V)
Electric potential, denoted as V, is the amount of electric potential energy per unit charge at a point in an electric field. It is a scalar quantity that indicates the work done to move a charge from a reference point to a specific point in the field without any acceleration. The shape of the graph in the question shows how the potential varies along the x-axis due to the influence of the point charges.
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07:33
Electric Potential
Point Charges
Point charges are idealized charges that are considered to be concentrated at a single point in space. They create electric fields and potentials around them, which can be analyzed using Coulomb's law. In this scenario, the charges qₐ and qᵦ at positions a and b affect the electric potential V along the x-axis, and their magnitudes and signs determine the shape of the potential graph.
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Ratio of Charges
The ratio of charges |qₐ/qᵦ| is a dimensionless quantity that compares the magnitudes of two point charges. This ratio can be derived from the electric potential at specific points in the field created by these charges. Understanding this ratio is crucial for solving the problem, as it relates the strengths of the electric potentials at points a and b to the respective charges.
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Related Practice
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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Textbook Question
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.
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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 two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot?
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Textbook Question
Four small spheres, each charged to +15 nC, form a square 2.0 cm on each side. From far away, a proton is shot toward the square along a line perpendicular to the square and passing through its center. What minimum initial speed does the proton need to pass through the square of charges?
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