Download Visual and Mathematical Representations of the Electric

Buggé: Electric Fields 1
Visual and Mathematical Representations of the Electric Field
1.1 Represent and reason. For each situation pictured in the table that follows, represent gravitational force
or the electric force that the object of source mass or source charge exerts on the object of test mass or test
charge at the points shown.
a) Use a field approach to explain in words how the source object can exert a force on test objects without
directly touching them at each of these points. For the gravitational field, discuss how the magnitude of
the force may depend on the properties of the field, on the mass of the source object, and on the
distance away from the source object. Consider similar factors for the electric field.
b) Discuss how the presence of a source mass or a source charge alters the space. How far do you think
this alteration extends?
c) Discuss whether a system that includes Earth and the test object possesses gravitational potential
energy. Discuss whether a system that includes the source charged object and the test charged object
possesses electric potential energy. Does each energy depend on the magnitude of the source mass or
the test mass? On the source charge or the test charge?
Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen
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Buggé: Electric Fields 1
Did you know?
We cannot see electric fields created by charged objects; we only know about the field’s presence at different
locations by placing other charged objects at these locations. The presence of the field is induced by how the
motion of the charged object is changed. We call the objects that probe the field test charged objects (or simply
test charges) and the objects causing the field source charged objects (source charges). The test charge has to
be small so that it does not alter the location of the source charges creating the field.
Physicists define two quantities to describe the field produced by a source electric charge in the space
surrounding the charge. For a particular point in that space, one field quantity is related to the force that the
field exerts on a test charge placed at that point. (This is a VECTOR quantity). The other field quantity is
related to the electric potential energy that a test charge has at that point (this depends on the choice of zero
level of potential and is a scalar quantity). We use the name, electric field intensity or simply, electric field for
the first quantity and the name electric potential (V field) for the second.
1.2 E-Field Lab
1. Go to http://phet.colorado.edu/en/simulation/charges-and-fields
Once the simulation is open, a green box in the bottom right hand corner will appear. Click on “grid” and a
grid will appear on the screen. Above the green box there is a box for E-field sensors, and 1 nC positive and
negative source charges. (Remember: nC = 10-9 C)
Place a positive source charge at any position on the grid. Then place the E-field sensor at various positions
around the source charge, click on “Show E-field” and observe the arrow. Place the positive 1nC back into the
red box and take out a negative source charge. Again, place the E-field sensor at various positions, click on
“Show E-field” and observe the arrow.
a) Discuss how the arrow is consistent with the process for finding the E-field at a point in space near a
given source(s)? Why are the arrows part of the simulation?
b) Place multiple sources on the screen; what happens to the arrow? What else can we conclude about the
arrow?
c) How does the magnitude of the E-field at any point A depend on the source charge? Test charge? The
distance between the source charge and point A?
Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen
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Buggé: Electric Fields 1
1.3 Practice: There are three charged particles below. For each of the dots (A,B,C), represent the E field at
that given point with labeled vectors.
C
B
A
Q=+q
Q= -2q
Q=+q
1.4 Diagram Jeopardy. E field vectors due to one or more electrically charged objects are shown below.
Indicate with circles, including the + or – signs, the charged source objects creating the field.
a.
b.
Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen
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Buggé: Electric Fields 1
Electric Field Lines An E field can be represented with E field lines. They have the following properties.
•
•
•
•
The direction of the E field line at a point is in the same direction as the E field at that point.
E field lines start on positively charged objects and end on negatively charged objects.
The magnitude of the field at a point is represented by the density or concentration of the lines near that
point.
A corollary to this idea is that the number of lines leaving or termination on the charged object is
proportional to the charge.
1.5 Reason. Examine the definition above and answer the following questions on E field lines.
a) Can E field lines ever cross?
b) What is the direction of the E field directly between two positive equal magnitude charged particles?
Explain why this happens. Draw an example
c) What is the direction of the E field directly between two negative equal magnitude charged particles?
Explain why this happens. Draw an example.
Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen
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Buggé: Electric Fields 1
1.6 Electric field Hockey (Electric field hockey is a property of the University of Colorado)
On the computers, go to. http://phet.colorado.edu/en/simulation/electric-hockey Answer the questions that
follow.
a) Set the difficulty to practice. When you drag a positive charge out of the bin on the top right and put it
on the hockey table, which direction is there an arrow pointing from our black test charge? Why does it
point in this direction?
b) Drag a Negative charge out of the bin and place it on the field. You will notice the arrow that comes
from the test charge points towards this new charge placed on the table. How does the arrow’s length
depend on the distance between the source charge and the test charge? Is the relationship linear? Why
does it exhibit this pattern?
c) Position the source charges so you can shoot the test charge into the goal. Press start and try it out.
d) With a single positive and negative charge on the table separated by about an inch, click the box that
says “Field.” Describe the direction the clear/white arrows on the table point. What do you think these
“Field” arrows represent?
e) Using a few combinations of charges, try to score goals on all three of the difficulty settings. (Don’t let
the puck leave the table). Take screenshots of your goals and email them to me
([email protected]).
Lessons are modified from the Active Learning Guide, Etkina and Van Heuvelen
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