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Lecture 2: Electric Fields and Electric Flux
January 23, 2025
Reading Assignment
- Read: The rest of 20.4, 20.5 (stop at “Dipoles in Electric Fields” on p. 381), 21.1-21.3
- Study: Eq 20.7; Ex 20.7; Eqs 21.1, 21.2 and 21.3
- Skim: “Dipoles in Electric Fields" in Section 20.5
Objectives
- (Continuing objective) Describe applications of the concepts of electricity and magnetism to everyday “real-life” situations.
- Relate the electric force on a charge to the electric field at the location of the charge.
- From a physical sketch or verbal description of a continuous line or line segment of charge, perform the following steps in setting up the calculation of the electric field at a given point \(P\). (a) Make a sketch, and choose a coordinate system and an integration variable. (b) On the sketch, mark a “non-special” piece of charge \(dq\), and label its size using \(dx\) or \(dy\) or \(Rd\theta\) as appropriate. (c) Generate correct expressions for \(r\) and \(dq\), in terms of the integration variable. Substitute these expressions into \(dE = kdq/r^2\) to determine \(dE\) from the marked piece of charge. (d) Determine the correct limits of integration. (e) Determine the geometric factors by which \(dE\) should be multiplied to get the components \((dE)_x\) and \((dE)_y\). (f) Integrate \((dE)_x\) and \((dE)_y\) to find the components of the total electric field.
- Represent and interpret electric fields using both field line and vector field diagrams.
- Use Gauss's Law to relate electric flux through a closed surface to the net enclosed charge.
Homework
- Friday's Assigned Problems:
A7, A8; CH 20: 34; CH 21: 1, 2, 3, 15, 19
Answers: CH 20 #34 (a) 1.35 cm; (b) proton momentarily comes to rest, reverses direction, then accelerates and exits the field region with speed $3.8 \times 10^{5}\, \mbox{m/s}$
- Monday's Hand-In Problems from Lecture 2:
X2 (below); CH 20: 32, 76;
CH 21: 14, 20
Note: this is only the second half of the hand-in set.
Problem X2 A thin rod lies on the $x$-axis with one end at $x=0$ and the other end at $x=L$. The rod carries a total charge $Q$ distributed uniformly over its length. Determine the electric field at a point on the $x$-axis at position $x=D$, where $D>L$.
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 6; CT2 - 1; CT3 - 3; CT4 - 3
- Step-by-step approach to E-field integration and useful integrals.
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 #1: Worked-out example of finding electric field from a rod.
- Example of finding electric field at the center of a ring of charge.
- Example of finding electric field from a curved arc. (Note: there are a few mistakes here, but they are soon corrected.)
- Example of an electric flux calculation with and without Gauss' Law.
Pre-Class Entertainment
- I Can't Help Myself - The Four Tops
- Run, Baby, Run - Sheryl Crow
- September - Earth, Wind, and Fire
- Think - Aretha Franklin
- Spell on Me - The Belairs
Assigned Problems Guide
- A7: long electric field integral problem. Much of the setup is like the example we did in lecture. You'll need to calculate both $E_x$ and $E_y$ (symmetry doesn't help you here).
- A8: medium long arc electric field integral problem. Some new setup issues, but fortunately once you get the integral set up, the math is simpler!
- 20-34: medium length. You can find the force right away, and then use work-kinetic energy to answer the rest.
- 21-1: quick conceptual problem.
- 21-2: fairly quick conceptual problem.
- 21-3: fairly quick conceptual problem.
- 21-15: medium length flux calculation. The electric field isn't uniform, but it is always perpendicular to the surface, and does have a constant magnitude.
- 21-19: quick Gauss's law problem, once you understand how to apply Gauss's law.