11. Capacitors and Dielectrics

• Course Home
• Syllabus
• Electric Fields

  • 1. Introduction to Electric Fields
  • 2. Math Review, Fields
  • 3. Electric Fields and Discrete Charge Distributions
  • 4. Electric Fields and Continuous Charge Distributions
  • 5. Gauss's Law
• Electric Potential

  • 6. Discrete and Continuous Distributions of Charge
  • 7. Equipotential Lines and Electric Fields
  • 8. Gauss's Law and Configuration Energy
• Capacitors

  • 9. Conductors and Insulators, Conductors as Shields
  • 10. Capacitance and Capacitors, Energy Stored in Capacitors
  • 11. Capacitors and Dielectrics
• Circuits

  • 12. Current, Current Density, Resistance, and Ohm's Law
  • 13. Batteries and Circuit Elements
  • 14. DC Circuits
  • 15. DC Circuits with Capacitors
• Magnetic Fields and Forces

  • 16. Magnetic Field
  • 17. Magnetic Forces
  • 18. Magnetic Dipoles
• Creating Magnetic Fields

  • 19. Biot-Savart Law
  • 20. Ampere's Law
• Faraday's Law

  • 21. Faraday's Law
  • 22. Inductance and Magnetic Energy
  • 23. RL Circuits
• Oscillating Circuits

  • 24. Undriven RLC Circuits
  • 25. Driven RLC Circuits
• Maxwell's Equations

  • 26. The Displacement Current and Maxwell's Equations
  • 27. Poynting Vector and Energy Flow in a Capacitor
• Electromagnetic Waves

  • 28. Maxwell's Equations and Electromagnetic Waves
  • 29. Energy and Momentum in Electromagnetic Waves
  • 30. Generating EM Waves, Dipole Radiation and Polarization
• Nature of Light

  • 31. Interference
  • 32. Diffraction
• Download Course Materials

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Learning Objectives

• To comprehend the properties of dielectrics that cause a change in the capacitance of the capacitor when a dielectric is inserted into its interior.
• To be able to state Gauss's Law when dielectrics are present.

Preparation

Course Notes

Read through the course notes before watching the video.  The course note files may also contain links to associated animations or interactive simulations. 

Read sections 5.5 through 5.11:
Capacitance and Dielectrics (PDF)

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

Problem Solving Help

Watch the Problem Solving Help videos for insights on how to approach and solve problems related to the concepts in this module.

Problem 1: Capacitor with Dielectric

A parallel plate capacitor with plates of area one square meter contains a dielectric slab that completely fills its volume. The electric field between the plates is 1.4x10⁶ Newtons/Coulomb. The dielectric slab has a dielectric constant k = 4.5. What is the free charge density on the plates of the capacitor and what is the induced charge density on the dielectric slab? What is the total energy stored in this capacitor?

Problem 2: A Cylindrical Capacitor with and without Dielectric

A cable consists of an inner conducting wire of radius a, charge q, and length l. It is surrounded by a thin outer metal cylindrical shell of radius b, carrying charge of –q. Calculate the capacitance of this cylinder in the case where there is a vacuum between the inner wire and the outer cylinder. We now fill the space between the inner wire and the shell with dielectric oil with dielectric constant k = 2.2. What is the capacitance now? When we bring the oil into the capacitor, will it be pulled in or pushed out?

Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

• Creating Electric Fields
• Creation of an Electric Dipole
• Creating an Electric Field
• Destroying an Electric Field
• Scattering of Charges of Opposite Sign
• Scattering of Charges with Same Sign
• Molecules
• Interactive Molecules 2D
• Interactive Molecules 3D
• Many Interactive Dipoles
• The Ion Trap
• Lattices 3D
• The Suspension Bridge
• The Suspension Bridge 3D

 

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