Mapping Potentials
PHYS 126 Lab #3
Ryan Johnston
rsjohns1@ualberta.ca
CCIS 2-102
Learning Goals
Learn about electric
fields and potentials
Track equipotential lines
on a sheet of paper and
visualize them
Learn to use a multimeter
to measure Voltages (as
a Voltmeter)
Potential Energy
Potential energy is stored energy that can be converted
into motion (kinetic energy).
● Gravitational potential energy is stored in an object you lift
up, you can then release that energy by dropping it.
●
𝑈𝑔 = 0
𝑈𝑔 → 𝐾
𝑈𝑔 > 0
Potential Energy
●
Zooming out, we see the
gravitational potential varies
in multiple directions out
from Earth’s Surface.
●
Gravitational potential
around the
Earth varies as you move
out radially.
●
Equipotential lines are
contours that
represent constant potential
energy.
Electric Potential
●
Analogous to gravitational potential energy in a gravitational field,
we can measure electric potential energy in an electric field.
●
We typically talk about potential difference V rather than electric
potential energy Ue.
●
Parallel plate capacitors generate a uniform electric field (except at
the edges).
●
Placing a charge in this electric field gives it a certain amount of
potential.
𝑈𝐸
𝑉=
𝑞
Coulomb’s law - recall!
𝑞1
+
+
+
+
++ +
+
+
𝑞2
+
+
Coulomb's law
𝐹𝑒
𝐹𝑒
𝑟
𝑘𝑞1 𝑞2
𝐹𝑒 =
𝑟2
– – –
–
–
–
–
–
–
–
–
Electric fields lines
<
<
+
+
+
+
Electric field lines are representations of the
direction of the electric field in a system
<
<
+
+
+
+
++ +
<
Electric fields lines
– – –
–
–
–
–
–
–
–
–
<
<
Electric field lines are representations of the
direction of the electric field in a system
<
Electric fields lines
>
<
+
+
+
+
++ +
+
+
>
+
+
>
>
>
Electric field lines are representations of the
direction of the electric field in a system
– – –
–
–
–
–
–
–
–
–
<
Electric fields lines
+1C charge
+
+
+
+
𝐹𝑒
++ +
+
+
>
+
+
>
>
>
– – –
–
–
–
–
–
–
–
–
Trace of the force experienced
by an unit charge
𝐹Ԧ𝐸 = 𝑞𝐸
Electric field lines are representations of the
direction of the electric field in a system
Equipotential points – Whaaaat?
>
<
+
+
+
+
++
+
+1V
+
+
+
+
+10V
+1V
+1V
>
>
+1V
>
+1V
>
-1V
– – –
–
–
–
–
–
–
–
–
<
One can also measure electric
potential energies at various
points
Lines along which potential is a constant
Equipotential points – Whaaaat?
>
<
+
+
+
+
++ +
+
+
>
+
+
>
>
– – –
–
–
–
–
–
–
–
–
<
>
Note: Equipotential lines are perpendicular to the direction of electric
field (use this property to your advantage in your analysis!)
Setup for analysis
Step 1: Choose a conductive
paper to work with.
There are a few shapes
available!
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Setup for analysis
Step 1: Choose a conductive
paper to work with.
There are a few shapes
available!
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Setup for analysis
Step 1: Choose a conductive
paper to work with.
There are a few shapes
available!
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Setup for analysis
Step 1: Choose a conductive
paper to work with.
There are a few shapes
available!
All of them are interesting in
their own ways!
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Setup for analysis
Step 2: Once you choose
your conductive paper,
connect the negative and
positive leads to the pins and
complete the circuit.
Set the Power supply to 4.5
Volts!
Get the multimeter
connected and ready for
measurement!
Make sure you are in volts
and DC mode on multimeter!
Credit: William Morrish
Setup for analysis
Step 2: Once you choose
your conductive paper,
connect the negative and
positive leads to the pins and
complete the circuit.
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Get the multimeter
connected and ready for
measurement!
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Power
Multimeter
Procedure
Step 3: Record the potential
values at the grid points.
You don’t have to measure all
the grid points but just enough
to trace the equipotential lines
of interest.
If you have time later, measure
all the grid points.
Power
Multimeter
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Setup for analysis
Based on the potential map,
trace equipotential lines for
voltages 1V, 2V, 3V and 4V
Feel free to interpolate the
data: if you have two grid
points at +3.9 V and +4.1 V,
you would draw the contour
for +4 V in between those
two points.
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Setup for analysis
Trace a few electric field
lines. You can not measure
this using the multimeter.
Equipotential lines are
perpendicular to the electric
field. Use this property to
trace the electric field lines
qualitatively.
Start by tracing line
perpendicular to the
potential lines and connect
them to complete!
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Setup for analysis
Show direction on the
electric field lines!
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One last analysis
On at least 5 grid points and
calculate the electric field
strength. Also, estimate
uncertainty.
ΔV
Vf − Vi
E=−
=−
Δs
sf − si
Δ𝑠: Distance between grid
points
𝑉3 − 𝑉1
𝐸=−
s3 − s1
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Uncertainty
Rulers: Take half-the
smallest measurable
division.
Note: You still estimate the
value in between the mm
tick lines when taking
measurements!
Digital Multimeter: Take ±
the smallest digit!
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Uncertainty
Two separate measurements!
𝑉𝑓 − 𝑉𝑖
𝐸=−
Δ𝑠
One measurement
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Uncertainty
You will need to use these
two equations from Table 6.1
in the Lab Manual
𝛿(Δ𝑉) = 𝛿(𝑉𝑓 + 𝑉𝑖 )
=
𝛿
𝛿𝑉𝑓
2
+ 𝛿𝑉𝑖 2
Δ𝑉
Δ𝑠
Δ𝑉
=
Δ𝑠
𝛿(Δ𝑉)
Δ𝑉
2
𝛿(Δs)
+
Δs
2
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Assignment
Submit a single PDF. 4 page limit.
● Use different colors for potential and electric field
lines.
● Remember to draw the directions for electric field
lines.
● When calculating field strength for at least 5 points,
include a table of data with a proper caption.
● Estimate the uncertainty in the electric field. Describe
the factors that influence the uncertainty.
●