# 11. Capacitors and Dielectrics

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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.

Capacitance and Dielectrics (PDF)

## Lecture Video

### Video Excerpts

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## 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?

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» iTunes U (MP4 - 18MB)
» Internet Archive (MP4 - 18MB)

### 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?

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