Electric field simulations
5/20/2009
Electric Field simulations
Go to the link http://cs.clark.edu/~mac/PHSC101/lessons17-24.htm and click on the button
“ChargesAndFields”. Select grid (check box), Show field, and show numbers .
Place a single +1 nC charge 2.5 m from the top
and 2.5 m from the left as shown (click and
drag). Let’s refer to this location as the origin
(x=0, y=0) Use an E-field sensor to probe the
Electric field.
Describe the electric field around this charge:
What is its direction?
And how does its magnitude change with
distance from the charge?
Our text states the electric field surrounding a
+Q point charge is:
E  ke
Q
radially outward
r2
Does this simulation environment agree with
this formula? Give three specific examples to
support your claim and record them in the table
below. Also show on the figure at left where
you measured the E field with the sensor for
each example. (ke=8.99x109 Nm2/C2)
Example #
E from sensor (magnitude and
direction)
E  ke
Q
r2
1 (r= 0.5 m )
2 (r= 1.0 m )
3 (r= 2.0 m )
The electric field is also defined to be the gradient of the electric potential, V. The electric potential is
often referred to as the voltage measured in Volts. That is, directly above +Q it has a magnitude of Ey=V/y and has a direction perpendicular to the equipotential lines from high to low potential. (If the
electric potential decreases as one moves in the positive y direction Ey is positive)
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Clark College Physics
Electric field simulations
5/20/2009
Use the voltage meter
to measure V and the grid scale for y to estimate the electric field
along a straight line above the charge at y=0.50 m, 1.00 m, and 2.00 m. For example, if you want the
electric field 1.0 m above the charge, find V at 0.95 m and V at 1.05 m, take the difference, and divide by
0.10 m. The actual positions above and below the point in question (1.0 m in this case) are not crucial
but should be symmetrically located about the point.
Example #
E from Ey=-V/y
Y=0.50 m V1=
Y=1.00 m V1=
Y=2.00 m V1=
V2=
V2=
V2=
E  ke
Q
r2
y=
y=
y=
Do the two methods agree? Actually in this case we are not redefining the Electric field but rather we
are providing a definition the electric potential, V, measured in volts. The electric potential is a scalar
quantity and the electric field is a vector.
Analogy with gravity:
Gravity
Gravitational Force F  G
Electricty
M1M 2
r2
The gravitational field of earth g  G
QQ
Electrical Force F  ke 1 2
r2
The Electric Field around Q
ME
r2
E  ke
2
g=9.8 m/s when r=RE
Gravitational Potential Energy U=mgy
(Uniform g field)
Gravitational potential Vg=gy (this is rarely
used)
Q
r2
Electric potential energy U=qEy
(uniform E field)
Electric Potential V=-Ey
(V is similar to the height for gravitational fields)
Electric potential energy U=qV
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Electric field simulations
5/20/2009
**Now go to http://www.mhhe.com/physsci/physical/giambattista/electric/electric_fields.html and
set up the system as shown below, with a fixed +1 charge on the x-axis at x=-150, and a test charge on
the x-axis at x=-100. (show grid, snap to grid, rubber walls, and show potential contours should be
selected)
Press Play and describe the motion in your own words. Is the collision with the wall elastic?
What is the initial Kinetic energy (when the test charge is at x=-100)?
What is the initial potential energy?
Fill in the table for values of Kinetic Energy(K), Potential Energy(U), Electric Potential(V), and total
Energy(E):
(Selecting slow speed gives a finer spatial resolution for your values, and using pause and step allows
you to get pretty precise results.)
Position
K
U
V
E
-100
-50
0
50
100
150
200
The electric potential at each point is found by moving the cursor around to different pints when Test is selected.
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Clark College Physics
Electric field simulations
5/20/2009
Using Excel, graph the electric potential versus distance from fixed charge r=(x+150). (V on y axis r=on
horizontal). Add a power law trendline fit.
What formula do you get for V as a function of r?
Create an electric dipole in the Electric Fields Tutorial Environment as shown below. Use alt/PrintScreen
to copy this to the clipboard and then past it into word and then print it out. With a pencil or pen,
highlight the +1.0 , +0.5 , +0.2 , 0, -0.2, -0.5 and -1.0 Volt equipotential lines in this diagram and then
draw 6 electric field lines leaving +Q and going into –Q. (remember the E-field should be perpendicular
to the equipotential lines .
What is the direction of the electric field along the x axis?
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Clark College Physics
Electric field simulations
5/20/2009
Using the “ChargesAndFields” Environment create a line of charges as shown.
What is the direction of the electric field to the right of the center of this line of charges?
What is the direction of the electric field to the right of the center of this line of charges?
What is the magnitude of the Electric field 0.5 m to the right of the center of these charges?
What is the magnitude of the electric field 1.0 m (twice as far) to the right of the center of these
charges?
What is the magnitude of the electric field 1.5 m to the right of the center of these charges?
From these three data values, how does the electric field depend on distance along a line to the right of
the center of these charges?
On the Figure above sketch the 60V and 40 V equipontential lines. Remember, like contour lines on an
elevation map, the equipotential lines should never cross and should either go off the page or come
back onto themselves. This is easy to do if you use the plot feature from the voltage probe
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Clark College Physics
Electric field simulations
5/20/2009
Using the Electric Fields Tutorial Environment, at a +Q at along the x-axis at -100 and +100 as shown
below. Use a test charge to explore the equilibrium at x=0. Remember an equilibrium point is where
F=0 and it is stable if when an object is released near the equilibrium point, the object tends to
oscillate around the equilibrium point.
Try these tests.
What happens when a + test charge is released
from any point on the x-axis?
What happens when a + test charge is released
from any point on the y-axis?
What happens when a - test charge is released
from any point on the x-axis?
What happens when a - test charge is released
from any point on the y-axis?
Is x=0 a stable equilibrium point? Discuss and explain.
Here we explore changes when you put two more
+Q at y=+100 and y=-100?
What is the approximate shape of the
equipotential lines when you are far from the
center?
Are there any stable equilibrium points for the four charge system when using a + test charge?
________ If so where?
Are there any unstable equilibrium points for the four charge system when using a + test
charge?________ If so where? (Hint: there is at least one unstable point along a line that goes 45
degrees between the x and y axes. Se if you can find it. )
What happens when you use a – test charge?
a. The equilibrium points stay the same.
b. The stable equilibrium points become unstable and the unstable become stable.
c. Neither a nor b.
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