Phys 223, Labatorial 2, Winter 2016
University of Calgary
Department of Physics and Astronomy
PHYS 223, Winter 2016
Labatorial 2: Electric Fields and Motion of Charged Particles
Goals:
• to understand how the electric field of several point charges is created by superposition
• to understand general properties of electric field vectors and of electric field lines
• to understand the relationship between field lines and force vector for various fields (uniform and
non-uniform)
• to understand the trajectories of charges moving in electric fields
Overview:
• construct the electric field of various configurations of point charges by using superposition
• use simulations to check your answers
• determine if a given figure of electric field vectors or electric field lines is correct or not
• draw the force on a charge in a given electric field, uniform and non-uniform
• predict the trajectory of a charge in a given electric field
• play electric field hockey
Preparation:
Randall D. Knight, Physics for Scientists and Engineers, Third Edition, Pearson/Addison-Wesley: sections
25.5, 26.1-2.
Equipment:
Applet charges generator, developed using the resources available on the Davidson University website
http://webphysics.davidson.edu; the “Electric Field Hockey” simulation, developed by the PhET Interactive
Simulations Project at the University of Colorado, http://phet.colorado.edu/en/simulation/electric-hockey,
distributed under the Creative Commons-Attribution 3.0 license.
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Phys 223, Labatorial 2, Winter 2016
Review Questions
Question 1: How do you find the electric field lines from the field vectors?
Question 2: How do you find the electric field vectors from the field lines?
In each of the following questions, determine whether the statement is true or false. If it is true, explain
why. If it is false, explain why, and give a counter example.
Question 3: “The more charges you put together in a region of space, the stronger the electric field gets.”
Question 4: “Electric field lines never cross.”
Question 5: “Electric field vectors never cross.”
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Phys 223, Labatorial 2, Winter 2016
Question 6: “Electric field lines always have to be straight.”
Question 7: “Electric field vectors always have to be straight.”
Question 8: “A charged particle in an electric field always moves along the field lines.”
Question 9: “The motion of a charged particle in a uniform electric field is always a straight line.”
CHECKPOINT 1: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 2, Winter 2016
The electric field vectors of a configuration of point charges
Question 10: At each point indicated by an ×, draw the individual electric field vectors due to the two positive charges, labeling which is which. In a different colour, draw the net electric field vector at each point ×.
The following questions will require you to use the applet charges generator to explore the electric field
generated by a series of point charges.
Question 11: Set up the configuration of two positive charges shown below and sketch the electric field
lines into the diagram provided. Are these field lines consistent with your prediction in Question 1?
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Phys 223, Labatorial 2, Winter 2016
Question 12: Now add another charge halfway between the two, as in the diagram below, and sketch the
electric field lines.
Question 13: Now add two more charges into the two gaps, as in the diagram below, and sketch the electric
field lines.
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Phys 223, Labatorial 2, Winter 2016
Question 14: What do you notice about the electric field above and below the line of charges as the number
of charges increases?
Question 15: Do electric field lines ever cross? Explain how you know using the idea of superposition.
Question 16: What would you expect the electric field to look like for a string of positive charges without
any spacing? Sketch this in the diagram below and verify using the applet.
CHECKPOINT 2: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 2, Winter 2016
Question 17: Figure 5 shows electric field lines for a nonuniform field. Draw the electric field vectors for
each of the points indicated by a dot.
Question 18: The figure below shows charges A-F, and the field lines between them. If charge D is negative,
what are the signs of the other charges? Show the directions of the electric field lines.
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Phys 223, Labatorial 2, Winter 2016
Conductors in electric fields
In the following questions, you will be asked to decide whether the representation of an electric
field shown in a figure is correct or not. The conductors are assumed to be in electrostatic
equilibrium.
Question 19: The figure below shows three charged conductors (there might be other charges nearby that
are not shown) and some electric field lines drawn by a student. Find all the errors in the figure, circle them,
and explain why they are errors.
Question 20: The figure below shows three charged conductors (there might be other charges nearby that
are not shown), and some electric field lines drawn by a student. Find all the errors in the figure, circle
them, and explain why they are errors.
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Phys 223, Labatorial 2, Winter 2016
Question 21: Four students were asked to represent the electric field in a parallel plate capacitor by drawing
field vectors. Their answers are shown below. For each student’s answer state whether it is wrong or right
and explain why.
Student A:
Student B:
Student C:
Student D:
CHECKPOINT 3: Before moving on to the next part, have your TA check
the results you obtained so far.
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Phys 223, Labatorial 2, Winter 2016
Motion of a charged particle in a uniform electric field
Question 22: For the points A-C shown in the figure below, draw the force that a positively charged particle
would experience.
--
+
+
+
+
y
x
+
A
---
B
-C
--
Question 23: In the figure below, draw the trajectory that the particle would follow in this field if it started
from rest at point A.
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Phys 223, Labatorial 2, Winter 2016
Question 24: In the figure below, draw the trajectory that the particle would follow in this field if it started
at point A with an initial velocity in the positive x-direction. Explain how you constructed the trajectory.
Question 25: In the figure below, draw the trajectory that the particle would follow in this field if it started
at point A with an initial velocity in the negative y-direction. Explain how you constructed the trajectory.
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Phys 223, Labatorial 2, Winter 2016
Motion of a charged particle in a nonuniform electric field
Question 26: For the points shown in the figure right, draw the force that a positively charged particle
would experience.
Question 27: A group of students was asked to draw the force on a negatively charged particle in the
electric field shown in the figure right. For each of the answers A-C, state whether it is correct or not, and
why.
Answer A:
Answer B:
Answer C:
Last Checkpoint! Clean up your area, and put the equipment back the way
you found it. Call your TA over to check your work and your area before
you can get credit for the labatorial.
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