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.