6. Discrete and Continuous Distributions of Charge

• 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
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Learning Objectives

• To be able to describe the physical meaning of the electric potential.
• To be able to describe the meaning of the work done in moving an electric charge in an electric field, and to be able to relate that concept to the electric potential.
• To be able to calculate the electric potential due to a set of point charges.
• To be able to calculate the electric potential of a uniform electric field.

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 3.1 through 3.4:

Electric Potential (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: Electron Moving in an Electric Field

An electron is shot at t = 0 with a speed of v = 2.5x10⁶ meters/second into a homogeneous E field of 1x10³ Newtons/Coulomb in the direction that causes it to slow down.

1. Sketch E and v in their relative configuration.
2. How far will the electron travel?
3. How long a time will it take for the electron to return to its original position?
4. Suppose now that the E field ends after only 10 millimeters. What fraction of the kinetic energy was lost in passing through the field?

Problem 2: The Potential of Two Opposite Charges

A negative charge -q sits on the positive y-axis at a distance a from the origin, and a positive charge +q sits on the negative y-axis at the same distance a from the origin. What is the electric potential everywhere on the y-axis?

 

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