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Lecture 2: Electric Fields
January 22, 2026
Reading Assignment
- Read: 20.3-20.5 (stop at “Dipoles in Electric Fields” on p. 381)
- Study: Eqs 20.2a, 20.2b, 20.3, 20.7; Exs 20.4, 20.5, 20.7
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.
- For a point charge or a configuration of several point charges, calculate the electric field (magnitude and direction) at any given location.
- 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.
Homework
- Friday's Assigned Problems:
A5, A6, A7, A8, X1 (below); CH 20 17, 23
Problem X1 A $65\,\text{$\mu$C}$ point charge is at the origin. Find the electric field at the points (a) $x=50\,\text{cm}$, $y=0\,\text{cm}$, (b) $x=50\,\text{cm}$, $y=50\,\text{cm}$, (c) $x=25\,\text{cm}$, $y=-75\,\text{cm}$.
Answers: X1 (a) $2.3\times 10^6\hat\imath\,\text{N/C}$, (b) $(8.2\times 10^5\hat\imath + 8.2\times 10^5\hat\jmath)\,\text{N/C}$, (c) $(3.0\times 10^5\hat\imath - 8.9\times 10^5\hat\jmath)\,\text{N/C}$
- Monday's Hand-In Problems:
X2 (below); CH 20 26, 32, 34, 76
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 $D>L$.
- A5 [phet.colorado.edu]
This simulation will allow you to look at the electric field produced by several point charges. Start by dragging three
positive charges (red dots) and an E-Field Sensor (orange) on to the page. Select “Electric Field” and “Values” (Note
that the unit of V/m is the same as N/C). Arrange the charges roughly into equilateral triangle.
- Where do you think the electric field will be the largest? Why? Use the E-Field Sensor to verify your prediction.
- Where will the electric field be zero? Why? Use the E-Field Sensor to verify your prediction.
- Optional Problem [www.physicsclassroom.com]
(Warning: this one is a bit addictive -- it's a game.)
This simulation contains a “goal” and a small blue positive test charge. By adding and relocating point charges, try to make a
goal. You can use “Clear Screen” to remove any point charges on the screen and “Reset Charge” to move the test charge back to
its starting position. Arrows show the magnitude and direction of the electric field.
- Click, “Choose Level” and select “1”. Where do you have to position a positive test charge to score a goal? Now clear the screen. Where do you have to position a negative charge to score a goal?
- Click “Choose Level” and select “2”. Using a combination of positive and negative charges, position enough charges that you can score a goal. Watch the motion of the test charge and compare it to the direction of the electric field. What can you conclude about the relationship between the electric field and the motion of the test charge?
Lecture Materials
- Click here for the Lecture overheads. Answers: CT1 - 3; CT2 - 1; CT3 - 6; CT4 - 1
- 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.- Fields and forces on charges.
- Vector addition of fields.
- Finding the electric field from a rod.
- Finding the electric field at the center of a ring of charge.
- Finding the electric field from a curved arc. (Note: there are a few mistakes here, but they are soon corrected.)
Pre-Class Entertainment
- In My Life - The Beatles
- Keep it Coming Love - K.C. and the Sunshine Band
- Is This Love? - Bob Marley
- Me and Bobby McGee - Janis Joplin