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Sierzega: Electric Fields 1
Electric Fields
Did You Know?
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 (a vector quantity). The other
field quantity is related to the electric potential energy that a test charge has at that point (this one
depends on the choice of the zero level of potential energy and is a scalar quantity). We use the
name electric field intensity or simply electric field ( E field) for the first quantity and the name
electric potential (V field) for the second.
E field: To determine the physical quantity called E field at a point, you need to place a
small positive test charge qtest at that point. Then measure or calculate the electric forces that
other electrically charged objects exert on it, find the sum of these electric forces, and divide
it by the magnitude of the test charge:
Felectrically charged objects on qtest
E=
qtest
If the E field at a point is due to only a single source charge qsource, then the E field equals
the electric force exerted on a test charge qtest by the source charge qsource at that point divided
by the test charge:
Fq source on qtest
E =
qtest
1.1 E-Field Lab 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.
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?
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1.2 A small aluminum ball is charged with +1.0 x 10-9 C. Determine the magnitude of the E
field due to this source charge at the four points shown below. Represent the E field at each
point using an arrow. Use the simulation to predict the magnitude and direction of the E field at
each point.
5 cm to the right of
the ball
+
7 cm to the left of
the ball
+
1 cm above the ball
10 cm below the
ball
+
+
1.3 Reason
Place two +1 nC sources at one position on the
grid. Three meters away place three -1 nC
sources. Predict the magnitude and direction of
the E-field vector 1 m to the left of the negative sources and then 1 m to the right of the negative
sources.
1.4 Reason
Place a +1 nC source at one position on the grid, move down 2 meters and
to the right 2 meters and place a -1 nC source there. Predict the E-field at
one of the corners of the 2 m x 2 m square.
1.5 Reason
Place three positive charges around a 2 m x 2 m square and predict what the
E-field will be in the empty corner and again in the middle of the square.
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1.6 There is a 1.24 g object near Earth that has an excess of charge on it. There is a uniform E
field directed downwards of magnitude 475 N/C. What must the excess charge (sign and
magnitude) be in order for the object to remain stationary?
1.7 A charged object with charge -6 nC remains at rest at position x = +1.0 m.
a) Find the magnitude and direction of the E -field at x = +0.6 m.
b) At what location(s) does the E -field have a magnitude of 4 N/C?
1.8 A charge, q1 = 5.0 µC, is at the origin, and a second charge, q2 = -3.0 µC, is on the x-axis
0.80 m from the origin.
a) Find the electric field at a point on the x-axis 0.400 m from the origin.
b) Find the electric field at a point on the y-axis 0.400 m from the origin.
1.9 Two charged objects of +5q and -q are placed at positions y = +0.0 m and y = +0.5 m,
respectively.
a) Determine the E -field at position y = +0.25 m.
b) Find the location at which the E -field is zero.
1.10 A -2.5µC and a +6.0 µC charged objects are 1.0 m apart from each other. Determine the
point (other than an infinite distance away) at which the total electric field is zero.
Did You Know?
Electric field lines: An E field can be represented with E field lines. They have the following
properties:

E field vector at a point is tangent to the direction of the E field line.

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 terminating on a charged object
is proportional to the magnitude of its electric charge.
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1.11 Represent and Reason
Draw E field vectors and E field lines for the electric field created by the source charged
objects described in the table that follows. Explain the difference between vector and line
representation and how the vectors help you draw the lines.
(a) A point-like
positively charged
object.
(b) A point-like positively
charged object with twice
the magnitude of charge as
in (a).
(c) A point-like
negatively charged
object.
(d) A point-like
negatively charged
object with twice the
magnitude of charge as
in (c).
(g) A small positively
charged object and a
small negatively
charged object of equal
magnitude charge
separated by a distance
s.
(h) A small positively
charged object and a
small negatively
charged object with
twice the magnitude
electric charge separated
by a distance s.
+
+
(e) Two positively
charged point-like
objects of equal
magnitude charge
and separated by a
distance s.
(f) Two negatively charged
point-like objects of equal
magnitude charge and
separated by a distance s.