PHY 2426 - Engineering Physics II
Equipotential Surfaces and Electric Field Lines
Leader:
___________________ Recorder:
__________________________
Skeptic:
___________________ Encourager:
________________________
Materials
Electric
Field Mapping Apparatus with parallel plates
3 x
Point Probes
DMM
2
Sheets Quadrille Graph paper (one laminated)
4 x
Banana plug cables
15” Ruler
Introduction
In this lab 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.
The magnitude of the average electric field
between two points separated a distance Dx is given by Eave = DV/Dx (1), where DV 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?
Q2) Using equation (1), what is the average
electric field between two points where the potential difference is 0?
An equipotential surface is a surface along
which the potential is the same everywhere.
Q3) What is the potential difference between any
two points on an equipotential surface?
Q4) What then is the average electric field
between any two points on an equipotential surface?
Q5) On the figure if the plates are charged as
shown, indicate the direction of the electric field at the point P.
Q6) The positively charged plate will have a
higher potential difference than the negatively charged plate. Do electric field lines point from higher
potentials to lower or from lower to higher?
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.
Q7) Explain why the static electric field inside
a conductor in electrostatic equilibrium is 0?
Q8) 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?
Q9) 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 in cm for 10 grids and divide
by 10. Record the spacing between the
grids on the graph paper in the space below.
Q10) 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. We will refer to the conducting plate connected to
the + terminal of the power supply as the + conductor and the conducting plate
connected to the – terminal of the power supply as the – conductor. 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
2. Setup the DMM
Connect the COM lead from the digital
multimeter (DMM) to the remaining point probe.
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
3. Preliminary
Measurements
Place the point probe connected to the COM
lead on the DMM on the - conductor.
Count 5 grids from the center of the – conductor towards the + conductor
and place the tip of the VΩ lead on the DMM and record the potential
difference.
Leave the COM lead on the – conductor and
move the tip of the VΩ lead 5 more grids and record the potential
difference. Repeat two more times so
that the tip of the VΩ lead ends up touching the + conductor.
Figure
2 Data Table for Potential Difference
|
Position
of COM Probe |
Position
of VΩ Probe |
ΔV |
|
0
(- conductor) |
5 |
|
|
0 |
10 |
|
|
0 |
15 |
|
|
0 |
20
(+ conductor) |
|
From
the data you recorded in figure 2, determine the potential difference between
points 5 grids apart between the conducting plates
Figure
3 Data Table for Potential Difference
between points 5 grids apart
|
Position
Lower Potential Point |
Position
of Higher Potential Point |
ΔV |
|
0
(- conductor) |
5 |
|
|
5 |
10 |
|
|
10 |
15 |
|
|
15 |
20
(+ conductor) |
|
4. Record Equipotential lines
We will record the equipotential lines
that we find directly onto the provided sheet of graph paper.
Place the probe connected to the COM lead
of the DMM on the grid centered on the conductors and located 5 grid lines
below the + conductor as indicated in figure 4.
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 COM
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 COM probe 5 grids down and use
the same procedure to find another equipotential surface.
Again move the COM probe 5 grids down and
use the same procedure to find another equipotential surface.
Figure
4 Location of the COM probe for the first
set of data
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 between points 5 grids
apart (Figure 3)
3. Three sets of data for equipotential surfaces
with the COM probe placed 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.
Q11) Describe the shape of the equipotential lines
in the interior of the capacitor.
Q12) 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 - conductor and label each of the
equipotential lines (including the conductors) with their respective
potentials. Note, you have measured
potential differences, not potentials.
Q13) 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.
Q14) What can
you conclude about the electric field in the interior of a parallel plate
capacitor?
Q15) Describe how electric field lines are related
to equipotential surfaces.