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 36c
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.
Verified step by step guidance1
Understand the relationship between electric potential (V) and electric field (E). The electric field is the negative gradient of the electric potential: Eₓ = -dV/dx. This means the slope of the V(x) graph determines the value of Eₓ.
Analyze the graph of V(x) provided in FIGURE EX25.36. Identify regions where the slope is positive, negative, or zero. A positive slope corresponds to a negative Eₓ, a negative slope corresponds to a positive Eₓ, and a zero slope corresponds to Eₓ = 0.
Determine the locations of the charges qₐ and qᵦ on the x-axis (at x = a and x = b). Near these points, the electric potential will exhibit steep changes, indicating strong electric fields. The direction of the field depends on the sign of the charges.
Sketch the graph of Eₓ as a function of x. For each region of the x-axis, use the slope of the V(x) graph to determine the magnitude and direction of Eₓ. Ensure that the graph reflects discontinuities or sharp changes near the charges, as the electric field is strongest near the charges.
Label the graph appropriately, marking key points such as x = a and x = b, and ensure the behavior of Eₓ aligns with the physical principles of electric fields and potentials. For example, Eₓ should point away from positive charges and toward negative charges.
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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 how much work would be done to move a charge from a reference point to a specific point in the field without any acceleration. The potential due to point charges can be calculated using the formula V = k * (q/r), where k is Coulomb's constant, q is the charge, and r is the distance from the charge.
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Electric Potential
Electric Field (E)
The electric field, represented as E, is a vector field that describes the force exerted per unit charge at any point in space due to electric charges. It is defined as the negative gradient of the electric potential, meaning that E = -dV/dx in one dimension. The direction of the electric field is away from positive charges and towards negative charges, indicating the direction a positive test charge would move in the field.
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Relationship Between Electric Potential and Electric Field
The relationship between electric potential and electric field is fundamental in electrostatics. The electric field is derived from the electric potential by taking the spatial derivative, which shows how the potential changes with position. This relationship allows us to graph the electric field as a function of position by analyzing the slope of the potential graph; where the potential decreases rapidly, the electric field is strong, and where it is flat, the electric field is weak.
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Related Practice
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
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
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|?
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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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