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Physics Lab 212
Electric Fields and Superposition: A Virtual Lab
NAME:
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LAB PARTNERS:
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LAB SECTION:
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LAB INSTRUCTOR: __________________________
DATE:
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EMAIL ADDRESS:
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Equipment List
N/A
Computer Software List
EM Field
Microsoft Excel
Physics Pre-lab 212
Electric Fields and Superposition
Name:__________________________
Section:_____
Date:__________
(Read this & answer the questions before coming to lab)
Summary of relevant concepts:
(a) The electric field at any point in space is defined as the force experienced by a test charge of
+1 C. Hence, the magnitude of the electric field at a distance r from a SINGLE point charge
Q is given by Coulomb's Law:
Q
Ek 2
where k = 8.99 x 109 Nm2/C2.
r
(b) The electric field from a COLLECTION of POINT charges is given by the vector sum of
the electric fields from all the individual point charges (“superposition”).
(c) Electric field lines provide a convenient way of visualizing the electric field in any region of
space:
 Electric field lines originate at positive charges and terminate at negative charges;
 The electric field at any given position is tangential to the electric field line;
 The spacing between electric field lines is inversely proportional to the strength of the
electric field: i.e. they are closer together where the field is stronger, and further apart
where the field is weaker.
(d) A common arrangement of charges in Nature is the electric dipole. This consists of two
charges equal in magnitude Q but of opposite sign, separated by a distance a. An electric
dipole is characterized by the dipole moment p= Qa. This is a vector that points from the
negative charge towards the positive charge.
Pre-lab Questions:
Q1. An important principle that you learnt about in lecture is “superposition.” The use of
superposition depends on a clear understanding of vector sums. What is the vector sum of the
three vectors shown below? They all have the same magnitude.
1200
1200
1200
Magnitude of resultant vector = _________________________
Direction of resultant vector = ___________________________
Q2. The figure below shows 4 positive charges of equal magnitude arranged on a semicircle
centered about the origin. What is the direction of the net electric field produced at the origin?
Direction of electric field = _______________________________________
y
450
450
x
Now, use superposition to calculate the direction and magnitude of the electric field at a point P
that lies on the perpendicular bisector of an electric dipole. (See figure below.) Your goal is to
first determine the electric field at any general value of r, and then in the limit r >> a.
P
r
-Q
+Q
a
Q3. In the diagram above, draw vectors that represent the electric field produced at P by each
charge. Also, draw a vector that represents the net electric field produced by the sum of these
two vectors.
Q4. From the vector diagram that you used above, derive an exact expression for the magnitude
of the electric field at P. The only parameters in your final expression should be the dipole
moment p = Qa, the distance r, the distance a and the constant k from Coulomb's Law. Call this
expression "Equation 1." (You will need it in the lab activity.)
Q5. Simplify your analytical expression for E(r) for large distances i.e. r >> a. You should
obtain a particularly simple expression. Call this expression "Equation 2." (Needed later in lab
activity.)
Q6. A rule of thumb calculation (no calculators!). Suppose you are at some distance r from an
electric dipole, such that r is much larger than the dipole separation a. You measure the
magnitude of the electric field from the dipole to be 0.001 N/C. If you double your distance from
the dipole, approximately what is the magnitude of the electric field?
Lab Activity 1: Electric Field From A Collection of Point Charges
In this first activity, we’ll use a program called EMFIELD to visualize the electric field created
by different arrangements of point charges.
 Start the EMFIELD from the EMField program group under the Physics group in the
START menu.
 From the "Display" menu, select "Show grid" and "Constrain to grid";
 From the "Sources" menu, select "3D point charges";
 From the array of positive and negative charges at the bottom of the screen, select
appropriate charges and position them to represent the arrangements shown in each
question below.
 From the "Fields and potential" menu, select the "Field vectors" option. When you
click at any point on the screen, the program will now show you the electric field vector
at that point.
 Set up the charge arrangement shown in the figure below in which the 8 point charges are
arranged on the corners of two concentric squares. The small square has a body diagonal
length equal to half the length of the side of the large square. The x and y axes bisect the
sides of the large square and pass through the vertices of the small square as shown. Use
the EMFIELD program to answer the questions on the following page.
 A word of caution: the program makes mistakes in regions where the electric field is very
small! Use physical intuition and common sense in interpreting your results!
(Warning: if you are using the lab template, you will need to save your figures to the
desktop and then insert them into your lab report. Cutting and pasting from the EMField
program can result in an error and a loss of any unsaved work!)
+1 C
+1 C
-1 C
+1 C
-1 C
A
B
+1 C
-1 C
-1 C
C
Q1. Suppose an electron were released from rest from positions A, B and C. Using EMFIELD,
figure out the DIRECTION and RELATIVE MAGNITUDE of the instantaneous force
experienced by the electron when its is released from position A, B and C. In the figure on the
previous page, draw vectors that represent these forces, with the lengths drawn proportional to
the magnitudes.
Q2. Creative exercise: Discuss below how you would answer this question without resorting to
the software program. Think about exploiting any symmetry that you see in the problem.
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Lab Activity 2: Modeling the Electric Field of a Water Molecule
A very common charge arrangement in Nature is the electric dipole in which two equal but
opposite charges Q and –Q are separated by a small distance a. Many types of molecules (e.g.
water) act like electric dipoles and may be characterized by the "dipole moment" p = Qa. Note
that this is a vector that (by definition) points from the negative to the positive charge. A water
molecule has zero net charge, but it produces an electric field around it similar to the electric
field of a dipole. The figure below shows a model of a water molecule, with the three nuclei
represented as black dots and the electron clouds represented as spheres.
HYDROGEN
Dipole
Moment
p
OXYGEN
Q3. Refer to the figure above: explain qualitatively why a water molecule acts like an electric
dipole. (Think about the charge distribution in the model above.)
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A. Visualizing the electric field from a dipole.
Now, we’ll use EMFIELD to plot the electric field from a dipole.
 From the "Sources" menu, select "3D point charges";
 From the array of positive and negative charges at the bottom of the screen, select a
positive charge and drag it to a position somewhere near the middle of the screen.
 Select an appropriate negative charge and position it to form a dipole.
 From the "Fields and potential" menu, select the "Field vectors" option.
Q4. Use the program to find out the DIRECTION of the electric field vectors at positions P1,
P2, P3 and P4 in the diagram below. Based on your observations, sketch in the figure below
arrows that represent the FORCE experienced by a proton at positions P1, P2, P3 and P4. Note
that P2 and P4 lie on the perpendicular bisector of the line joining the charges.
P4
P1
+Q
-Q
P2
P3
From the "Fields and potential" menu, select the "Field lines" option. When you click on any
point on the screen, you will see an electric field line that passes through that point. You can use
this option to construct an electric field line plot for your electric dipole. Note that electric field
line plot is only meaningful if you obey the proper rules! Specifically, electric field lines should
be closer together where the electric field is stronger, and further apart where the electric field is
weaker.
Q5. If you randomly click at any point on the screen, EMField will plot an electric field line
passing through that point. So, you could create an electric field line plot by selecting any
number of random points on the screen. Try this! Why is the resulting electric field line plot not
particularly meaningful? Describe a strategy that will help you make a correct plot of electric
field lines. Again, remember the basic rules!
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Q6. Make a meaningful plot of the electric field lines from an electric dipole. Print out your plot
and include it with your lab report. Observe the characteristics of your electric field line plot.
How are the electric field vectors related to the electric field lines?
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Q7. Do electric field lines ever intersect?
Explain your answer briefly.
Yes
No
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B. Numerical Calculation of the Electric Field of a Water Molecule
Q8. A good model for the water molecule is to consider it as a dipole with two charges of +10e
and –10e, where e is the charge on an electron (since that's the total number of electrons or
protons in the molecule). If the dipole moment of the molecule has a magnitude
p = 6.2 x 10-30 C m, what is the separation between the two charges in this model?
A numerical calculation helps to visualize how this dipole field varies with distance. Open the
spreadsheet dipfield.xls in the Movies folder.
Q9. Use equation 1 that you derived in the prelab to tabulate the magnitude of the electric field
E(r) of the water molecule. Plot E(r) versus r using a log-log scale. Include a hard copy of the
table & plot with your lab report. Explain briefly why it is not convenient to use a standard
linear scale in the plot.
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Q10. Creative exercise: use the plot in Q9 to determine how large r needs to be for Equation 2
to be accurate. Relate this scale with the dipole parameter a.
Physics Post-lab 212
Electric Fields and Superposition
Name:__________________________
Section:_____
Date:__________
Q1. Plot E(r) versus r using a log-log and a linear scale. Include a hard copies of the plots
with this post lab report. Remember to follow the guidelines for a scientific plot as
outlined in your laboratory manual. (Also, include your name in the plot titles, plots
without your name or with handwritten names will not be accepted for a grade.)
E( r ) [N/C]
1.10E-10
4.06E-12
3.20E-13
1.10E-13
3.25E-14
4.06E-15
3.20E-16
1.10E-16
4.99E-17
2.23E-17
r[Å]
1
3
7
10
15
30
70
100
130
170
Q2. Explain briefly why it is not convenient to use a standard linear scale in the above plot.
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