Chap22-ConDie
Chapter 22: Conductors and Dielectrics in Electrostatic Field
1. Key Concepts
Conductor: Material with many free-moving charges.
Examples: Metals like copper, silver.
Insulator: Material with almost no free-moving charges.
Examples: Rubber, glass.
Semiconductor: Material with electrical conductivity between that of a conductor and insulator.
2. Capacitance
Capacitance defines the ability of a capacitor to store charge.
Formula: C = Q/V, where C is capacitance, Q is charge, V is voltage.
3. Dielectrics
Materials that can store electric energy in an electric field.
When placed in an electric field, dielectrics can polarize, which affects capacitance.
4. Energy Stored in Electric Field
The potential energy stored in a capacitor relates to the voltage and charge.
Formula: U = 1/2 QV = 1/2 CV^2.
Page 1: Introduction to Conductors and Dielectrics
Overview of Electrostatic Field: Conductors, Capacitance, Dielectrics, Energies stored.
Conductor
Characterized by free-moving electrons, allowing charge to be distributed evenly across its surface.
Dielectrics
Insulating materials that separate charged plates in capacitors, influencing capacitance.
Capacitance
Describes a capacitor's ability to store charge as voltage changes.
Page 2: Charged Isolated Conductor
Conductor: Contains many free-moving charges.
Insulator: Contains almost none.
Semiconductor: Intermediate property.
Interaction with Electrostatic Fields
A conductor placed in a uniform electric field experiences forces on its charges.
Page 3: Electrostatic Equilibrium
Electrostatic Equilibrium: No net charge movement within conductor.
Free charges redistribute to counteract electric fields.
Electrostatic Induction: Redistribution of charges in response to external electric fields.
Page 4: Conditions of Electrostatic Equilibrium
The electric field must be perpendicular to the conductor's surface.
The electric field inside a perfect conductor must equal zero.
Charges settle on the outer surface due to the repulsion between like charges.
Page 5: Equipotential Nature of Conductors
Equipotential: All points inside and on the surface of the conductor maintain a constant potential.
No electric field exists within a conductor under electrostatic equilibrium.
Page 6: Charge Distribution in Conductors
Excess charge on isolated conductors distributes entirely on their surface.
Inside the conductor, the net charge is zero, confirmed by Gauss' Law.
Page 7: Surface Charge Density
The electric field just outside a conductor's surface is proportional to the surface charge density.
Relationship: E = σ/ε₀ where E is the electric field and σ is surface charge density.
Page 8: Isolated Conductor with a Cavity
No net charge on inner cavity walls unless charges exist within the cavity.
Any charge present induces an equal and opposite charge on the inner surface.
Page 9: Surface Charge Density and Curvature
Surface charge density is related to the radius of curvature of the conductor.
Higher charge density occurs at points of smaller radius (sharp edges).
Page 10: Electrostatic Shielding
Discusses how the electric fields of external charges do not penetrate the interior of a conductor.
Page 11: Charge Distribution in Conducting Shells
Analyzes charge placement when conductors are concentric.
Charge is distributed uniformly on the surface of the inner shell.
Page 12: Voltage and Potentials
Calculates potentials of connected spherical conductors.
Compares potential differences under different charging scenarios.
Page 13: Parallel Plate Capacitors
Explanation of surface charge density at each plate of the capacitor.
Relation between charges and resulting electric fields.
Page 14: Electric Fields in Capacitors
Discusses electric field behavior with ground-connected plates.
Relationship between electric fields and surface charge densities.
Page 15: Capacitors and Electronic Applications
Capacitance plays crucial roles in electronic circuitry (e.g. radios, TVs).
Page 16: Parallel Plate Capacitor Description
Two parallel conducting plates create uniform field and relationship between charge and potential difference.
Page 17: Capacitance Definition and Units
Capacitance depends on geometry and dielectric properties, not charge or voltage.
Standard unit: Farad (F).
Page 18: Calculating Capacitance in Parallel Plates
Discusses effective capacitance with area and separation considerations.
Introduces dielectric effects in parallel plates.
Page 19: Capacitance of Cylindrical Capacitors
Focus on configuration and geometry of cylindrical capacitors.
Page 20: Capacitance of Spherical Capacitors
Details about isolated spheres and how charge interacts.
Page 21: Capacitance with Dielectrics
Filling capacitors with dielectrics increases capacitance due to dielectric constants.
Page 22: The Role of Dielectric Constant
Explains the concept of dielectric constant introduced by Faraday.
Page 23: Capacitance Changes in Dielectrics
Capacitor design influences change in capacitance with insertions of dielectrics based on boundary field equations.
Page 24: Electric Fields with Dielectrics
Changes in electric fields due to dielectric materials present throughout electric distributions.
Page 25: Molecular Description of Dielectrics
Polar Dielectrics: Molecules with permanent dipoles.
Nonpolar Dielectrics: No permanent dipole moments.
Page 26: Effects of Dielectrics
Explains how dielectrics impact dipoles alignment in external fields.
Page 27: Polarization Effects
Describes polarization charges and fields generated within dielectrics under electric fields.
Page 28: Net Electric Field Inside Dielectric
The relationship showing the weakening of electric field magnitude within dielectrics.
Page 29: Gauss' Law Applied to Dielectrics
Addresses how Gauss' law maintains for systems with and without dielectrics.
Page 30: Electric Displacement in Systems
Describes electric displacement’s role in characterizing charge distributions and fields.
Page 31: Electric Displacement and Bound Charge
Discusses the distinction between bound and free charges regarding displacement laws.
Page 32: Parallel-Plate Capacitor Calculations
Practical examples of capacitor calculations with and without dielectrics.
Page 33: Electric Fields in Capacitors with Dielectrics
Analyzes the impact of dielectric installation on the electric field within a capacitor.
Page 34: Impact of Dielectrics on Capacitance
Examines how dielectric portions affect overall capacitance and electric potential differences.
Page 35: Work and Energy in Capacitors
Explains work done on capacitors and how it converts to energy stored as electric potential.
Page 36: Energy Distribution in Capacitors
Discusses how energy density relates back to the electromagnetic field dynamics in capacitors.
Page 37: Unit Volume Energy Density
Provides a formula around energy density related to the strength of electric fields.
Page 38: Electric Potential Energy in Fields
Relates electric potential energy to its distribution across multiple field scenarios.
Page 39: Coaxial Cable Field Configuration
Analysis related to charge distribution in coaxial cable structures and dielectrics.
Page 40: Capacitance in Coaxial Capacitors
Determines how geometry informs capacitance in coaxial set-ups.
Page 41: Energy of Electric Fields in Coaxial Capacitors
Various ways of calculating stored electrical energy across coaxial capacitor configurations.
Page 42: Energy Stored in Coaxial Capacitor
Investigates how potential energy ratio exists based on coaxial energy distributions.
Page 43: Chapter Problems
Problems relevant for self-assessment: 15, 19, 26, 48, 49, 50, 56, 57, 65, 84, 85.