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What is the capacitance of the two metal spheres shown in FIGURE EX26.22?
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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 21b
Two 3.0-cm-diameter aluminum electrodes are spaced 0.50 mm apart. The electrodes are connected to a 100 V battery. What is the magnitude of the charge on each electrode?
Guida verificata passo dopo passo1
Step 1: Recognize that this is a problem involving a parallel-plate capacitor. The charge on each electrode can be determined using the formula for capacitance and the relationship between charge, capacitance, and voltage: \( Q = C \cdot V \).
Step 2: Calculate the capacitance \( C \) of the parallel-plate capacitor using the formula \( C = \frac{\varepsilon_0 \cdot A}{d} \), where \( \varepsilon_0 \) is the permittivity of free space \( (8.85 \times 10^{-12} \ \text{F/m}) \), \( A \) is the area of one electrode, and \( d \) is the separation between the plates.
Step 3: Compute the area \( A \) of one electrode using the formula for the area of a circle: \( A = \pi \cdot r^2 \), where \( r \) is the radius of the electrode. The diameter is given as 3.0 cm, so \( r = 1.5 \ \text{cm} = 0.015 \ \text{m} \).
Step 4: Substitute the values for \( \varepsilon_0 \), \( A \), and \( d \) into the capacitance formula \( C = \frac{\varepsilon_0 \cdot A}{d} \) to calculate the capacitance.
Step 5: Use the calculated capacitance \( C \) and the given voltage \( V = 100 \ \text{V} \) in the formula \( Q = C \cdot V \) to find the magnitude of the charge \( Q \) on each electrode.
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Capacitance
Capacitance is the ability of a system to store electric 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 electrodes. In this scenario, the capacitance can be calculated using the geometry of the electrodes and the distance between them.
Video consigliato:
Percorso guidato
08:02
Capacitors & Capacitance (Intro)
Electric Field
The electric field is a vector field that represents the force exerted by an electric charge on other charges in its vicinity. It is defined as E = V/d, where E is the electric field strength, V is the voltage, and d is the distance between the charges. Understanding the electric field is crucial for determining how charges interact in the given setup.
Video consigliato:
Percorso guidato
03:16Intro to Electric Fields
Charge Distribution
Charge distribution refers to how electric charge is spread over a surface or within a volume. In the case of the electrodes, the charge will distribute evenly across their surfaces due to their symmetry. The total charge on each electrode can be calculated once the capacitance is known, using the relationship Q = C * V.
Video consigliato:
Percorso guidato
04:03Probability Distribution Graph
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