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PHYS 1402 – General Physics II
Introduction to Electric Potential and E-field Mapping
Leader: _____________________________ Recorder: ___________________________
Skeptic: _____________________________ Encourager: _________________________
Materials
Part I
2 x D cells
Pasco circuit kit
Socket with 3 V light bulb
4 x Alligator clip wire
Steel wool
Genecon
Digital Multimeter
Part II
Electric Field Mapping Apparatus with parallel plates
3 x Point Probes
Battery Eliminator
DMM
2 Sheets Quadrille Graph paper
4 x Banana plug cables
Ruler
Safety
If the D cells used in the following procedure ever got noticeably hot, immediately
disconnect any wires.
Introduction
In the first part of this activity we will investigate the idea of electric potential and its
relation to electrical energy. We will also use a DMM to measure electric potential and
observe the behavior of batteries when connected in series and parallel. In the second
part of the activity we will investigate the connection between electric potential and the
electric field by measuring surfaces of constant electric potential – called equipotential
surfaces – and using them to determine the electric field in a parallel plate capacitor.
Part I – Introduction to Potential
Procedure
Part 1 – Energy Transformations
Make sure that the cord is plugged into the Genecon, and turn the handle of the Genecon
at about 1 turn per second. Note: Do not turn the handle of the Genecon too hard as this
can strip the gears inside.
Q1) What type of energy does the Genecon handle have while you are turning it?
Q2) From where did it obtain the energy?
Connect the alligator clips on the cord together and turn the handle of the Genecon at
about 1 turn per second.
Q3) Did you have to exert a greater torque on the handle to turn it at the same rate when
the leads were connected together?
Q4) If you turn the handle at the same rate, does its kinetic energy change?
Q5) If you had to exert a greater torque, then did you have to do more work on the
Genecon?
Clearly, when you connect the leads from the Genecon together, the amount of work you
have to do increases, suggesting that the energy you are adding to the system is being
dissipated, but as what?
Disconnect the alligator clips and connect them on opposite sides of a single strand of
steel wool. Give the Genecon a couple of quick turns and observe what happens. If
nothing happens, make sure that the connection to the steel wool is good. If nothing
happens after several tries, contact your instructor.
Q6) Describe what you observed.
Q7) What was the source of the thermal energy that melted the strand of steel wool? (I.e.
where was the energy input?)
Connect the Genecon leads to opposite sides of the provided light bulb socket. Turn the
handle at about 1 turn per second and observe what happens. Note if the handle turns
very easily and nothing happens check your connections. If still nothing happens contact
your instructor.
Q8) Describe what you observe.
Q9) How is the light bulb lighting similar to the strand of steel wool melting? How is it
different?
Q10) What was the source of the thermal energy that causes the light bulb to glow? (I.e.
where was the energy input?)
As a historical note, Edison’s invention of the light bulb was not really the discovery
that if metal got really hot it glowed. The invention was finding a practical light bulb that
would last.
You should have observed that you were doing work on the handle and that the work
you did was being dissipated as heat by the light bulb. The Genecon is an energy
conversion device. It converts the mechanical energy of turning the handle into electrical
energy. The electrical energy is transmitted by charge flowing in the wire.
Q11) What does the light bulb do to the electrical energy?
Part 2 – Potential Difference
Place one of the D cells into a battery holder on the Pasco circuit board. The board has
connections which are made by attaching wires to the coils on the board. Attach a wire
from each side of the battery to a corresponding side of a light bulb socket. Disconnect
the light bulb after you make your observation to preserve battery life.
Q12) Describe what you see.
Q13) From where did the light bulb obtain the energy to light?
Q14) Did you do work on the battery so that it could provide the energy or was the
energy already stored in the battery (by some previous work)?
Q15) Another term for stored energy is __________ energy.
It turns out to be convenient in electricity that instead of talking about potential energy,
we refer to potential energy per charge. If a charge, q, experiences a difference in
potential energy, ΔU, between two points, then the Potential Difference, ΔV, between
those two points is defined as ΔV = ΔU/q. The SI unit for potential difference is the volt
for which the symbol is V.
Q16) If a battery is rated at 1.5 V, then across its terminals it provides 1.5 V of
__________ ___________, or 1.5 joules of ________________ per coulomb of
__________.
Part 3 – Measuring Potential Difference
In this part of the lab we will explore measuring potential difference and familiarize
ourselves with the use of a digital multimeter, DMM. A DMM is probably the most basic
tool for making electrical measurements.
The DMM has several sockets into which you plug the wires – known as leads. You
choose various sockets depending on what quantity you are measuring. You will always
plug one of the leads into the socket labeled COM. COM stands for common since it is
always used no matter what you measure with the DMM. To measure potential
difference, plug the black lead into the socket marked COM and the red lead into the
socket labeled V Ω. Turn on the DMM so that it will read DC volts. Simultaneously
place the red lead on the + terminal of a D cell and the black lead on the – terminal of the
same D cell.
Q17) Record your reading. Don’t forget units.
Q18) Reverse the side of the battery to which the leads are connected. How does the
reading on the DMM change?
A DMM when set up correctly is designed to that the lead connected to the V Ω socket is
at a higher potential than the lead connected to the COM socket when the measured
potential is positive.
Q19) Which terminal of the battery is at higher potential. Explain using your answer to
Q17 and Q18.
Some DMMs can measure AC as well as DC potential. A common error in using DMMs
with this capability is to have the DMM on the wrong setting when trying to measure a
potential difference. Switch the DMM to the AC Volts setting and measure the potential
difference across the battery.
Q20) Record the result.
Q21) If measuring a DC potential difference and you obtain 0 V, what is a good thing to
check on the meter?
Part 4 – Batteries in Series and Parallel
Place a D cell into the second battery holder. Connect the + terminal of one cell to the –
terminal of the second. Notice that the cells are connected one after the other. This type
of connection is known as a series connection. When multiple cells are connected
together, the combination is known as a battery.
Q22) Which terminals will be the + and – terminals of the battery? Explain.
Connect the battery across a light bulb.
Q23) How does the brightness of the light bulb now compare to the brightness when it
when it was connected to a single D cell? You may want to connect the light bulb across
a single D cell again for reference.
Q24) What does this suggest about the potential difference across a series combination of
cells compared to an individual cell.
Q25) Make sure that the DMM is on the DC setting and use it to measure the potential
difference across the battery. Record the result.
Q26) How does the measured potential difference of the battery compare to the measured
potential difference of the individual cell?
Get together with a nearby group and measure the potential difference for three cells
connected in series and then four cells connected in series.
Q27) Record your results. (Groups can separate now.)
Q28) When cells are connected in series, the potential difference of the combination is
the __________ of the individual potential differences.
Now connect the cells so that the + terminals are connected to each other and – terminals
are connected to each other. This combination of cells is referred to as a parallel
combination.
Connect the parallel combination across a light bulb.
Q29) How does the brightness of the light bulb now compare to the brightness when it
when it was connected to a single D cell? You may want to connect the light bulb across
a single D cell again for reference.
Q30) What does this suggest about the potential difference of a parallel combination
compared to an individual cell?
Q31) Which are the + and – terminals of a parallel combination of cells?
Q32) Use the DMM to measure the potential difference across the parallel combination
of cells. Record the result.
Q33) When identical cells are connected in parallel, the potential difference of the
combination is the ___________ of the individual cells.
Note only identical cells should ever be connected in parallel.
Q34) If we want a light bulb to be brighter we want to connect cells in __________.
Q35) Most graphing calculators have four 1.5 V cells connected in series. What
potential difference is the calculator using?
We will discuss what applications there might be for connecting batteries in parallel at a
later date.
Part II – Mapping the Electric Field
Introduction
In part I we have explored the meaning of potential difference and learned how to
measure it. In part II of this activity we will investigate the relationship between the
electric field and potential difference. We will do so by using potential difference to map
the electric field lines of a two-dimensional parallel plate capacitor. A parallel plate
capacitor consists of two parallel conducting plates separated by a small distance.
From the book we know that the magnitude of the average electric field between two
points separated a distance x is given by Eave = V/x (1), where V is the potential
difference between the two points. Thus by measuring the distance separating and the
potential difference between two points, we can determine the magnitude of the average
field.
Q1) The electric field is a vector quantity, so to completely specify it what must we find
besides the magnitude of the field?
To find the direction, we first note that the average field between any two points
where the potential difference is zero is also zero. An equipotential surface is a surface
along which the potential is the same everywhere.
Q2) What is the potential difference between any two points on an equipotential surface?
Q3) What then is the average electric field between any two points on an equipotential
surface?
We define the direction of the average electric field as that in which the potential is
changing most rapidly. This direction, it turns out, will always be perpendicular to the
equipotential surfaces. Also, by definition electric field lines run from a region of higher
potential to a region of lower potential. Thus, in this lab we will determine the electric
field by finding equipotential surfaces. The magnitude of the field will be determined by
measuring the potential difference and the distance between the equipotential surfaces,
and the direction of the electric field will be obtained by determining the direction
perpendicular to the equipotential surfaces.
Q4) What is the static electric field inside a conductor in electrostatic equilibrium?
Q5) If the static electric inside a conductor is 0, then is there a potential difference
between any two points in a conductor in static equilibrium?
Q6) Is a good conductor in electrostatic equilibrium an equipotential surface? Explain.
In the procedure below, we will use the fact that a conductor in electrostatic equilibrium
is an equipotential surface to help us map the electric field.
Procedure
The apparatus for this lab is sketched in figure 1. It consists of a plastic dish, several
probes, several stainless steel metal strips, graph paper, a power supply (battery
eliminator), and a digital multimeter (DMM). The DMM is an inexpensive and versatile
instrument which can be used to measure resistance, AC and DC current, and AC and DC
potential differences.
1. Set-up the Apparatus
To set up the experiment, first determine the scale of the graph paper by measuring
the spacing for 10 grid and divide by 10. Record the spacing between the grids on the
graph paper in the space below.
Spacing per grid = ________ cm/grid
Next, place the graph paper underneath the dish so that the grid lines run parallel to
the edges of the dish. Place the stainless strips with their long edges parallel to the long
edges of the dish, and so that their inner edges are aligned along grid lines separated by
20 grid lines. Place the tip of two of the probes on each of the conductors. Fill the dish
with water until the conductors are just covered by the water. Using the provided banana
plug cables, connect the + terminal of the power supply to one of the probes and the terminal to the other probe. It is customary to use a red wire for the connection to the
positive side, and a black wire for the connection to the negative side. Set the power
supply to 6 V and turn it on.
Figure 1 Schematic of experimental apparatus
Power Supply
DMM
2. Setup the DMM
Connect each of the probes from the digital multimeter (DMM) to one of the
remaining two probes. The connectors on the back of the probe will unscrew revealing a
hole in the connector that you can put the probe into. Tighten down the connector to hold
the probe and make a good contact. Turn the dial on the DMM to the 20 V DC setting.
The DC side is indicated by a solid line over several dashed lines. Place the probe
connected to the red probe on the DMM on the conductor connected to the plus side of
the power supply and the other probe connected to the DMM on the other conductor. The
meter should give a reading approximately equal to the setting on the power supply, if it
does not, contact your instructor.
3. Preliminary Measurements
In order to find the average electric field, we need to determine the potential
difference between the different equipotential lines. Record the positions of both the
inner corners of each of the conductors directly onto the second sheet of sheet of graph
paper. Place the probe connected to the + side of the DMM (red probe) on the plus
conductor and place the probe connected to the minus side (or common) of the DMM
(black probe) at a grid point centered on the conductors and located 5 grid lines below the
+ conductor as indicated in figure 3. Record the potential difference between these two
points in the data table below. Move the probe connected to the + lead to where the –
probe and move the – probe five grids down. Record the potential difference. Repeat
two more times. At the last point, the – probe should be touching the – plate.
Figure 2 Data Table for Potential Difference
Position of VΩ Probe
Position of common Probe
ΔV
3. Record Equipotential lines
We will record the equipotential lines that we find directly onto the graph paper.
Place the probe connected to the + side of the DMM on the grid centered on the
conductors and located 5 grid lines below the + conductor as indicated in figure 3. Move
the other probe to find 7 positions to each side of the plus probe (a total of 14 ponts)
where the potential difference between the two probes is as close to zero as you can find.
Record the locations of the + probe and these points on the second sheet of graph paper.
Find points that are roughly equally spaced horizontally and include at least three that
extend beyond the region between the two conductors on either side. This set of points
forms an equipotential surface.
Move the + probe 5 grids down and use the same procedure to find another
equipotential surface.
Again move the + probe 5 grids down and use the same procedure to find another
equipotential surface.
Figure 3 Location of the + probe for the first set of data
+
5
-
Data Analysis
Data Check
It is common for students performing this lab to not have all of the data. Your data
should include all of the following. If you are missing any data make sure you obtain it.
1. Spacing per grid on graph paper
2. Potential differences every five grid starting at + plate and ending at – plate
3. Three sets of data for equipotential surfaces with the + probe at 5 grid intervals
To analyze your data, connect the data points for the three different equipotential
surfaces with a smooth curve. Draw straight lines indicating the positions of the two
conductors between the points you recorded for the inside corners.
Q7) Describe the shape of the equipotential lines in the interior of the capacitor.
Q8) How does the shape of the equipotential lines change in the area exterior to the
capacitor?
Take the reference of potential to be 0 V on the minus conductor and label each of the
equipotential lines (including the conductors) with their respective potentials. Note, you
have measured potential differences, not potentials.
Q9) Inside the capacitor do the equipotential lines have about the same potential
difference between them? If the lines are equally spaced and equidistant, what does this
suggest about the electric field in the interior of the capacitor?
Your graph should now have 5 equipotential surfaces (remember the two plates are
equipotential surfaces) with four regions between the equipotential surfaces. Use
equation (1) to find the average field in each of these regions. The correct SI units for the
field are V/m but it is quite acceptable and more common use to use units of V/cm to
indicate the field strength. Draw a series of arrows on the graph in the correct direction to
show the electric field in the interior of the capacitor. Label the arrows with the field
strength. Remember the length of the arrows should be proportional to the field strength
and the direction should be perpendicular to the equipotential surfaces. Be sure to draw
arrows all along the equipotential surfaces to show how the direction changes. Also
remember that the field lines point from higher potentials to lower.
Q10) What can you conclude about the electric field in the interior of a parallel plate
capacitor?
Q11) Describe how electric field lines are related to equipotential surfaces.