Domanda del libro di testo
50 pJ of energy is stored in a 2.0 cm×2.0 cm×2.0 cm region of uniform electric field. What is the electric field strength?
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Ch 26: Potential and Field
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 26, Problema 32
A 2.0-cm-diameter parallel-plate capacitor with a spacing of 0.50 mm is charged to 200 V. What are (a) the total energy stored in the electric field and (b) the energy density?
Guida verificata passo dopo passo1
Step 1: Calculate the area of one plate of the capacitor. The diameter is given as 2.0 cm, so the radius is 1.0 cm (0.01 m). Use the formula for the area of a circle: A = πr².
Step 2: Determine the capacitance of the parallel-plate capacitor using the formula C = (ε₀A) / d, where ε₀ is the permittivity of free space (8.85 × 10⁻¹² F/m), A is the area of the plates, and d is the separation between the plates (0.50 mm = 0.0005 m).
Step 3: Calculate the total energy stored in the capacitor using the formula U = (1/2)CV², where C is the capacitance and V is the voltage (200 V).
Step 4: Compute the energy density (u), which is the energy per unit volume, using the formula u = U / Volume. The volume of the capacitor is given by the product of the area of the plates and the separation distance: Volume = A × d.
Step 5: Combine the results from the previous steps to express the total energy stored (U) and the energy density (u) in terms of the given values and constants.
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Capacitance
Capacitance is the ability of a capacitor to store charge per unit voltage. It is defined as C = Q/V, where C is capacitance, Q is the charge stored, and V is the voltage across the plates. For parallel-plate capacitors, capacitance can also be calculated using the formula C = ε₀(A/d), where ε₀ is the permittivity of free space, A is the area of the plates, and d is the separation between them.
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Percorso guidato
08:02
Capacitors & Capacitance (Intro)
Energy Stored in a Capacitor
The energy (U) stored in a capacitor is given by the formula U = 1/2 CV², where C is the capacitance and V is the voltage. This equation shows that the energy stored is proportional to the square of the voltage and the capacitance. Understanding this relationship is crucial for calculating the total energy stored in the electric field of the capacitor.
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Percorso guidato
09:26Energy Stored by Capacitor
Energy Density
Energy density (u) in an electric field is defined as the energy stored per unit volume. For a capacitor, it can be calculated using the formula u = 1/2 εE², where ε is the permittivity of the material between the plates and E is the electric field strength. This concept helps in understanding how energy is distributed within the electric field of the capacitor.
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Percorso guidato
8:13Intro to Density
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