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Lecture 3: Gauss's Law and the Electric Potential
January 28, 2025
Reading Assignment
- Read: 21.4-21.6, 22.1-22.2 through “Finding Potential Differences Using Superposition” (p. 421)
- Study: “Problem Solving Strategy 21.1” starting on p. 396, Exs 21.1, 21.3, 21.4, and 21.6; Eqs 22.1a, 22.1b, 22.3, 22.5; Exs 22.1, 22.5
Objectives
- (Continuing objective) Describe applications of the concepts of electricity and magnetism to everyday “real-life” situations.
- Use Gauss's Law to calculate the electric fields due to symmetric charge distributions.
- For a uniform electric field, relate \(\vec{E}\) to the potential difference between two points in the field.
- Calculate the electric potential for a system of point charges, using superposition.
- For a given physical arrangement of charges and fields, relate electric potential difference, potential energy change, work, and kinetic energy change.
Homework
- Wednesday's Assigned Problems:
A9, A11; CH 21: 7, 8, 27, 55; CH 22: 2, 39, 55
Notes: For CH 21 #27 and #55, show all the steps needed to clarify how you can get the field from Gauss's Law.
- Monday's Hand-In Problems from Lecture 3:
CH 21: 24; CH 22: 40, 44, 56
Notes: For CH 21 #24, show all the steps needed to clarify how you get the field from Gauss's law.
Note: this is only the first half of the hand-in set.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 1; CT2a - 1; CT2b - 6; CT3a - 1; CT3b - 3; CT3c - 2; CT4 - 4
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Example finding E-field for nested spheres, using Gauss's Law.
- Example finding the E-field for a problem with cylindrical symmetry using Gauss's Law.
- Example finding E-field near middle of a large sheet, using Gauss's Law.
- Example working with potential and potential differences.
Pre-Class Entertainment
- Ain't Too Proud to Beg - The Temptations
- Pomp and Pride - Toots and the Maytals
- Moondance - Van Morrison
- Ironic - Alanis Morissette
- Smooth - Santana
Assigned Problems Guide
- A9: medium. Use work-kinetic-energy, and get the work from the potential.
- A11: quick when you understand it. Relate plate potentials to electric field.
- 21-7: fairly quick conceptual problem.
- 21-8: fairly quick conceptual problem.
- 21-27: medium-long. Need to set up Gauss's law problem.
- 21-55: long and kind of tricky. Need to set up Gauss's law problem, and digest what they are telling you about the charge distributions.
- 22-2: quick conceptual problem
- 22-39: quick. Similar to A11.
- 22-45: medium-long and kind of tricky. You have a mixture of symbols and numbers. Use work kinetic energy and try to set up ratios.
- 22-55: medium-long. Use the point charge potential.