5.6: Dielectrics in Electric Fields

Learning Objectives

• Construct qualitative models to show the equilibrium state for charges in an insulator (dielectric) in the presence of a nonzero external electric field.
• Qualitatively model the electric fields created by the polarization of dielectrics due to external electric fields or charges.

5.6.1 Insulators (Dielectrics) in an Electric Field

Model

The model below shows the state of an insulator (dielectric) over time. Starting in the second panel, a constant electric field is applied.

Explore

1. When an electric field is applied to an insulator, what objects move? What direction do they move?
2. Are the charges able to move as far from their positive charges as in a conductor?
3. Describe the charge distribution (i.e., where they are located) when an external electric field is applied to an insulator.
4. Is the electric field zero inside an insulator? If not, is the electric field stronger or weaker than the applied electric field?

Critical Thinking & Concept Invention

1. For each attached pair of charges, what direction would the electric field they create point? How does that compare to the applied field?
2. Why does the electric field get weaker inside an insulator?
3. What is different about how charges respond to electric fields in an insulator, compared to a conductor?

Apply

Complete the models with the following:

• Draw the equilibrium charge distribution on the conductor and dielectric (insulator).
• Draw the electric field lines (if any) inside the conductor and insulator. If the electric field is zero, write: \[ \vec{E}=0 \]

Model

Explore

For each tape pair:

1. Draw the direction of the electric field vectors that are created by the charges shown on the left tape in the pair. If the field is zero, write: \[ \vec{E}=0 \]
2. Based on the direction of the electric field (if present), the electrons will move off of the positive charge. Identify which direction (right or left) the electrons will move and mark up the model to look like one of the provided options.

Critical Thinking & Concept Invention

1. The newly separated charges create their own field. In each pair, draw (using a different color if possible) the electric field on the left side of the right tape that is created by the charge nearest to that edge of the tape. If the field is zero, write: \[ \vec{E}=0 \]
2. Now draw the force on each charge of the left tape that is caused by the field from the right tape that you just drew. If the force is zero, write: \[ \vec{F}=0 \]
3. Below each pair, write Attracts, Repels, or No Interaction to describe the direction of these forces.
4. Summarize what you learned about charged-object and neutral-object interactions.

Model

Explore

1. In a vacuum, are the equipotential lines (vertical lines) evenly spaced or does the spacing change between potential lines?
2. How much does the voltage change between equipotential lines in this model?
3. Are there equipotential lines inside the conductor? What about the insulator? If so, is the spacing the same or different than outside of that material?

Critical Thinking & Concept Invention

1. Do different parts of a conductor have different electric potential values (voltages)?
2. Do different parts of an insulator have different electric potential values (voltages)?
3. How does the presence of a conductor affect the total number of potential lines between the charged plates? How does this affect the total difference in electric potential (positive minus negative) between the plates?
4. How does the presence of an insulator affect the total number of potential lines between the charged plates? How does this affect the total difference in electric potential (positive minus negative) between the plates?
5. If you wanted to reduce the voltage between two plates as much as possible, would you add a conductor or an insulator between them? Why?

Apply

Complete the models with the following:

• Draw the equilibrium charge distribution on the conductors and dielectrics (insulators).
• Draw the electric field lines (if any) inside the conductors and insulators. If the electric field is zero, write: \[ \vec{E}=0 \]
• Draw equipotential lines on both models. Make sure the spacing of the lines matches the established relationship between equipotential lines and electric field lines.

Model

Explore

1. Fill in the table with information from the model.

Critical Thinking & Concept Invention

1. For plates with the same charge, when dielectrics are added to a capacitor, do they increase or decrease the potential difference between the plates?
2. In order to get the same voltage as a capacitor without a dielectric, would you need to increase or decrease the amount of charge on each plate?
3. Summarize: Why do dielectrics affect the capacitance of a capacitor?

Summary

If a dielectric is added between the plates of a capacitor with an initial capacitance of \(C_0\), the new capacitance is:

\[ C=\kappa C_0 \]

The dielectric constant (\(\kappa\)) is a material property of the substance that is inserted between the capacitor plates.

Electricity does not flow through the dielectric (it is an insulator). This substance affects the electric properties of the capacitor and circuit as a whole by affecting the electric fields.