Domanda del libro di testo
An electron with an initial speed of 500,000 m/s is brought to rest by an electric field. Did the electron move into a region of higher potential or lower potential?
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Ch 25: The Electric Potential
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 25, Problema 18
A 250 pg dust particle has charge −250e. Its speed is 2.0 m/s at point 1, where the electric potential is V₁=2000 V. What speed will it have at point 2, where the potential is V₂=−5000 V? Ignore air resistance and gravity.
Guida verificata passo dopo passo1
Step 1: Recognize that the problem involves the conservation of energy. The total energy of the particle (kinetic energy + electric potential energy) at point 1 must equal the total energy at point 2, as no external forces like air resistance or gravity are acting.
Step 2: Write the expression for the total energy at each point. At point 1, the total energy is the sum of kinetic energy and electric potential energy: \( E_1 = \frac{1}{2}mv_1^2 + qV_1 \). At point 2, the total energy is \( E_2 = \frac{1}{2}mv_2^2 + qV_2 \).
Step 3: Set the total energy at point 1 equal to the total energy at point 2, as energy is conserved: \( \frac{1}{2}mv_1^2 + qV_1 = \frac{1}{2}mv_2^2 + qV_2 \).
Step 4: Rearrange the equation to solve for \( v_2 \), the speed at point 2: \( v_2 = \sqrt{v_1^2 + \frac{2q(V_1 - V_2)}{m}} \).
Step 5: Substitute the given values into the equation. Use \( q = -250e \) (where \( e = 1.6 \times 10^{-19} \ \text{C} \)), \( m = 250 \ \text{pg} = 250 \times 10^{-12} \ \text{kg} \), \( v_1 = 2.0 \ \text{m/s} \), \( V_1 = 2000 \ \text{V} \), and \( V_2 = -5000 \ \text{V} \). Simplify the expression to find \( v_2 \).
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Electric Potential Energy
Electric potential energy is the energy a charged particle possesses due to its position in an electric field. It is defined as the work done to move a charge from a reference point to a specific point in the field. The change in electric potential energy can be calculated using the formula ΔU = qΔV, where q is the charge and ΔV is the change in electric potential.
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Percorso guidato
07:51
Electric Potential Energy
Conservation of Energy
The principle of conservation of energy states that the total energy in a closed system remains constant. In the context of electric fields, the kinetic energy of a charged particle can convert to electric potential energy and vice versa. This means that the sum of kinetic energy and potential energy at one point must equal the sum at another point, allowing us to relate speeds and potentials.
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06:24Conservation Of Mechanical Energy
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity of the object. In this scenario, as the dust particle moves through different electric potentials, its kinetic energy will change in response to the changes in electric potential energy, affecting its speed.
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06:07Intro to Rotational Kinetic Energy
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