Phys1112K - Superposition and Standing Waves
Name:
Date:
TA’s Name:
Apparatus: PASCO mechanical vibrator, PASCO interface, string, mass hanger (50 g) and set of masses,
meter stick, electronic scale, two wire leads, pulley and two metal stands with brackets.
Objectives:
1. To understand superposition of two sinusoidal waves moving in opposite directions.
2. To study wave propagation in a string.
3. To understand the formation of standing waves on a string.
Part 1: Introduction
In your tutorial you studied the reflection and superposition of pulses moving in a slinky and in a string.
Here in this experiment you are going to investigate the superposition of two oppositely moving
sinusoidal waves moving in a tight string. When two sinusoidal waves of the same frequency are moving
in opposite directions in the same medium, a standing wave is the result. This often occurs when a wave
is traveling in a medium where there is a reflection at one or both ends.
Figure 1 shows a standing wave pattern resulting from periodic waves of wavelength λ traveling to the
right and to the left in the string. In a standing wave, there are points in the medium with zero
displacement called “nodes” where the two waves are always in destructive interference. There are also
points with maximum displacement called “antinodes” where the two waves are always in constructive
interference. The three lines shown in the standing wave pattern indicate the position of the string at
three different times in the motion; one when the entire string is at the equilibrium position (flat line),
one when the antinodes have a maximum displacement from equilibrium, and one when the antinodes
have a maximum displacement in the opposite direction from equilibrium.
1. Identify all nodes by marking them with the letter “N” and all antinodes by marking them with the
letter “A” in the standing wave pattern shown below.
Wavelength λ
1
Part 2: Fixed frequency with different tensions
2. In class you discussed the relationship of wave speed with tension. What did you learn from that?
Fix the string vibrator to a metal stand. Then take the string and attach one
end to the string vibrator. Connect the PASCO interface to the vibrator using
two wire leads. Connect the PASCO interface to the computer if it is not
already connected. Open up a template. Select the signal generator in the
menu locate to the left. Then click open controls of the signal generator and
select the frequency to be 60HZ and amplitude to be 6V. Switch on the signal
generator using the on/off button. Hold the free end of the string as shown in
the figure below and slowly increase the tension by pulling it away. Observe
the standing wave patterns that occur as you stretch the string.
PASCO vibrator
3. What happens to the number of antinodes as you increase the tension?
Wire leads
PASCO
interface
4. What happens to the wavelength as you increase the tension? Refer back to the figure on the first
page to see how wavelength is related to nodes and antinodes.
5. Does the frequency of the standing wave change as you increase the tension?
6. What is the justification to your answer in #5?
2
7. Adjust the tension until the string vibrates with 4 segments. Then adjust the tension slightly (fine
tune) so that you get a good node at the blade.
Good node at the vibrator end
Bad node at the vibrator end
Explain how you can tell that the displacement of the medium (string) is zero at nodes.
8. Measure and record the length of a segment or between two adjacent nodes using meter stick.
Length of a segment:
9. Determine the wavelength of the standing wave using a meter stick.
Wavelength = ______________________________
3
Part 3: Fixed tension with different frequencies
You just experimentally verified the existence of standing waves with nodes and antinodes. You also
observed that for a fixed length of a string the wavelength of a standing wave varies with tension in the
string. Now you are going to investigate the formation of standing waves in the string with different
frequencies at a fixed tension.
Now setup the apparatus as shown below. Make sure that the string is horizontal. Place 100 g in the mass
hanger so that the total mass attached is 150 g. Adjust the length between the pulley and the vibrator to
be more than 1.00 m. Connect the frequency generator to the string vibrator. The signal generator
generates sinusoidal waves and that signal is fed to the vibrator. Therefore the vibrator vibrates with
simple harmonic oscillations.
String
String Vibrator
Wire leads PASCO Interface
Pulley
Metal stand
Mass and hanger
Table
10. Now slowly increase the frequency of the signal generator using PASCO interface computer
controls used above starting at 0 Hz and carefully observe the formation of standing waves which
have a good node at the vibrator end. Once you reach such a frequency, fine tune it with fine
frequency adjustment. Complete the observation/measurement chart below.
Sketch of the standing wave pattern
# of antinodes
4
f (Hz)
λ (m)
fλ
11. The last column is the product of frequency times wavelength, fλ. What SI units does this quantity
have?
12. What kinds of quantities have the same units as does the frequency times wavelength?
13. Is the quantity fλ approximately the same for all these standing waves?
14. Based on the values in the last column calculate the average speed of the waves in the string?
15. Look at the frequencies you found that give good standing waves. Do you see a pattern for these
values? What relationship do you find between frequency and the number of antinodes?
16. Look at the wavelengths you found that give good standing waves. Do you see a pattern for these
values? Express the wavelength in terms of the length of the string and the number of antinodes.
5
Part 4: Same standing wave pattern with different tension
17. Transfer your data for standing wave with 3 antinodes using 150 g hanging mass to the table
below. Then repeat #10 with different tensions using 250 g and 350 g total hanging masses to
find the frequency which results in a good standing wave with 3 antinodes. Complete the table
below.
# of
antinodes
3
f (Hz)
mass=150 g
λ (m)
fλ
f (Hz)
mass=250 g
λ (m)
fλ
f (Hz)
mass=350 g
λ (m)
fλ
18. What can you conclude about how tension affects the wave speed? Is this consistent with what
you found in the previous experiment?
19. When the wave speed increases, will the wavelength need to increase, decrease or stay the same
to get the same standing wave pattern (such as the one with 3 antinodes)?
20. When the wave speed increases, will the frequency need to increase, decrease or stay the same to
get the same standing wave pattern (such as the one with 3 antinodes)?
Part 5: Application
21. Based on your experience in this experiment explain tuning a guitar (or any other stringed
instrument) by changing the tension of the string. (You explanation must be based on frequency,
wavelength, and speed of the wave)
6
Phys1112: Double Slit Interference
Name:
Warning: Never look into the laser.
Never shine the laser into someone else’s
eyes.
Slits are delicate and finding replacements is very
difficult. They come in little bags. Please be sure to
put them back into their bags before returning them
to the equipment cart at the end of the experiment.
Group Members:
Date:
TA’s Name:
Apparatus: A set of double slits, a slit holder, red and blue laser pointers, a laser pen holder, screen with
screen holder, meter stick, and plastic ruler.
Objectives:
1. To observe the formation of interference patterns due to a double slit.
2. To investigate and understand the parameters which determine the distance between bright
fringes in a double slit interference pattern.
Part 1: Introduction
Double slits
You have already discussed two-source interference in the class. Carefully inspect the double slits given
to you. The most important dimension of the double slit is the slit spacing or separation between slits,
“d.” There are 5 double slits with different “d” values.
When we shine monochromatic (single wavelength) light on the two slits, instead of observing an image
of the two slits, we observe bright and dark fringes on the screen (or wall). Also notice that the fringes
are spaced much further apart than are the slits. The number and spacing of these bright and dark
patches is very different than what we would expect if the light behaved just as rays. These bright and
dark fringes demonstrate the wave nature of light. Light traveling through different slits travels on
different paths but arrives at the same point on the screen and interferes to make the observed pattern.
Setting up the experiment
Setup the laser pointer and the slit as shown in the picture where the
pattern of light after passing through the slits is showing up on the
wall of the room.
In the class you learned that when light goes through a small opening
(such as single slit) it displays wave properties. Two light waves with
the same frequency and wavelength which travel on different paths
can interfere and make bright fringes with constructive interference
and dark fringes with destructive interference. With a double slit, light
traveling along different paths as it passes through each of the two slits
will interfere when arriving at the same point on the screen.
Practice lining up the laser to pass through single slits and double slits. Investigate the pattern of bright
and dark fringes produced by each of these double slits.
1
Part 2: Interference Patterns from Double Slits
1. Describe the pattern you observe when the red laser light passes through the double slit with
the smallest slit separation. Pay close attention to the fine detail.
2. Sketch the pattern you observe.
3. Now observe the pattern from the double slit with a larger “d” value. The closely spaced
fringes from the largest “d” value double slit are hard to notice because they are so close to
each other. Carefully describe what you observe.
4. Sketch the pattern you observe. Use approximately the same scale as the sketch in Question 2.
5. Compare the pattern you observe from the double slit with the smallest separation (“d” value)
with the pattern from the double slit with a larger separation. List similarities and differences.
Pay close attention to the fine detail.
Similarities:
Differences:
2
Part 3: Double Slits with Different Wavelengths
6. Make the following observations using two different color lasers. During your observations do
not make any changes to the distance (L) between the slit and the screen. We keep this
parameter constant for our first observations.
Color
Red
Sketch the interference pattern of each double-slit by drawing only the center
bright fringe and two more fringes on each side. Since we need to compare, pay
attention to relative center to center distance between the bright fringes when
drawing. Follow a same scale for drawing for comparison.
Smaller “d” value double slit
Larger “d” value double slit
Blue
7. Now name the fringes on your sketches in Question 6 as follows with an order “m.”
Central bright fringe: Zero order fringe or central maximum; m=0.
Two bright fringes (to the left and ant right) next to the central fringe: first order fringes; m=1.
Second set of two bright fringes: second order fringe etc.: m=2.
m=2
m=1
m=0
m=1
m=2
8. For the double-slit with smaller “d” value which color gave you the largest distance between
bright fringes?
9. For double slit with larger “d” value which color gave you the largest distance between bright
fringes?
10. Which double slit and color gave you the largest distance between the bright fringes?
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11. For the double slit and color you answered in Question 10, is the center to center distance
between any two consecutive (adjacent) bright fringes the same, that is, are the centers of the
bright fringes evenly spaced apart? Make some measurements before you decide and explain
your work below.
12. How does intensity (brightness) of the fringes change as you go from zero to higher orders?
13. Now select the color and slit which gave you the largest distance for bright fringes. Increase or
decrease the distance between the slit and the screen and observe what happens to the center
to center distance between the central fringe and the 1st order bright fringes. Record your
observations below.
4
Part 4: Testing a Mathematical Model for the Double Slit Interference Pattern
Based on the observations you made so far one of your colleagues suggests that the distance
between the centers of the bright fringes, can be expressed mathematically as follows.
λL
𝑦=
𝑑
where y = distance from center of one bright fringe to center of the next bright fringe
L = distance between the screen and the double slit
d = slit separation in the double slit
λ = wavelength of the light
This is a hypothesis that we need to investigate, but we have already done some experiments.
14. Is the hypothesis above consistent with the dependence of fringe separation on the wavelength
that you observed (that is, the data in the table in Question 6)? Explain how it is or is not.
15. Is the hypothesis above consistent with the dependence of fringe separation on slit separation
“d” that you observed (that is, the data in the table in Question 6)? Explain how it is or is not.
5
16. Is the hypothesis above consistent with the dependence of fringe separation on the distance
“L” between the screen and the slits that you observed (that is, your answer to Question 13)?
Explain how it is or is not.
17. In class you learned that “light is an electromagnetic wave and results of double slit
experiment can be explained as an interference pattern of light waves coming from two
sources.” That raises a question. You had only a single laser pointer. What were the two
sources that produced the interference pattern for a given color?
6
Phys1112: Lenses and Ray Tracing
Name:
Group Members:
Date:
TA’s Name:
Materials: Ray box, converging lenses, screen, lighted object, three stands, meter stick, two letter size
white pages, and pencil.
Objectives:
1. Understanding real image formation from lenses due to refraction.
2. Practicing ray tracing for converging and diverging lenses
3. Understanding magnification and using a lens combination to improve magnification
Part 1: Ray Tracing
1.
Draw a long straight line down the middle of a sheet of white paper to be our optical axis. Draw a
line perpendicular to the optical axis in the middle of the page to be our lens plane. Take the
thinner converging lens out from the box and place it on a white sheet of paper as shown below.
(DO NOT use the thickest one.) Now use the ray box to produce a single ray coming from the left
side of the lens running parallel to the optical axis. Notice that the ray is refracted by the lens and
changes direction. Trace onto the paper the path of the ray before and after going through the
lens and label this as Ray 1. Mark the point where the refracted ray crosses the optical axis with
an “F.” This point is the right side focal point of the lens. Be careful not to change the position of
the lens on the paper.
Left side of the lens
Right side of the lens
Ray 1
optical axis
Lens plane
2.
The shortest distance from the lens plane to the focal point is called the focal length. From your
ray diagram measure the focal length, f, of the converging lens. Remove the lens to do this but put
it back in place when done.
f = ____________________________________
Remember Units
1
3.
Now use a parallel ray coming from the right side of the lens to locate the focal point of the lens
on the left side. Also mark this point with an “F.” Is the focal length the same as you found in
Question 2?
4.
Send a ray from the left side of the lens through the left side focal point and into the lens as shown
below. Trace the ray onto the paper before and after it is refracted by the lens and label it on
your paper as Ray 2.
Ray 2
F
5.
After going through the lens, is the refracted Ray 2 parallel to the optical axis?
6.
Send a ray directly through the center of the lens and trace the ray. Label it as Ray 3 on your
paper.
Ray 3
7.
Summarize the behavior of each of these three rays (called principal rays) after they pass through
the converging lens.
Ray 1 – a ray parallel to the optical axis _________________________________________________________________
_______________________________________________________________________________________________________________
Ray 2 – a ray passing through the front-side focal point _______________________________________________
______________________________________________________________________________________________________________
Ray 3 – a ray passing through the center of the lens ___________________________________________________
______________________________________________________________________________________________________________
2
8.
Now we will use these three rays to construct a ray diagram in order to locate an image. On a
separate sheet of paper draw the optical axis and the lens plane. Use your measured value of the
focal length to mark the left and right side focal points and label them each “F.” Now draw an
arrow with its base at the optical axis which has a height, h, of 1.0 cm and is located 15.0 cm from
the center of the lens (15.0 cm will be the object distance, s). This arrow represents the object.
O
9.
F
F
We will use the ray tracing method to find the image. We do this by locating the image point for
the tip of the object. This tells us where the tip of the image must be. Use the ray box to create
Ray 1 which passes through the tip of the arrow and continues parallel to the optical axis until
striking the lens. Trace Ray 1 onto your paper both before and after passing through the lens.
Ray 1
O
F
F
10. Use the same technique to find Ray 2 (passing through the tip of the arrow and through the left
side focal point before striking the lens) and Ray 3 (passing through the tip of the arrow and then
through the center of the lens). Trace Ray 2 and Ray 3 onto your paper both before and after
passing through the lens.
11. Do the three refracted rays cross at a single point? Yes or No.
If not, do they cross nearly at the same point? Yes or No.
12. This crossing point is the location of the tip of the image. We know that the base of the object
must lie on the optical axis. Draw an arrow with its tip at the crossing point and its tail at the
optical axis to represent the image.
3
13. Is this image real or virtual? ___________________________
Explain your reasoning using the features of your ray diagram to support you answer.
14. Is the image upright or inverted? ___________________________________
Explain how you know.
15. Measure the height of the image, h’. If the image is inverted then make your image height
negative to indicate that image is inverted. Remember units.
h’ = ____________________________________________
16. The ratio
𝑚=
ℎ′
ℎ
ℎ′
ℎ
is called the magnification. What is the magnification?
= ______________________________________
Be careful with the units here!
17. The distance from the center of lens to the tail of the image is called the image distance, s’.
Measure it for your ray diagram.
s’ = ____________________________________________
𝑠′
18. Using geometry we can predict that the magnification will also be equal to 𝑚 = − 𝑠 . Use the
object and image distances to calculate M.
𝑚=−
𝑠′
𝑠
= ______________________________________
19. Is the value of magnification calculated from distances nearly the same as what you found using
the heights?
4
Part 2: Creating an Image with a Converging Lens
For this part of the experiment we investigate the creation of an image by a converging lens. You will be
changing the distance to the object from the center of the lens and measuring the image distance and
height. Set up the apparatus as show in the figure below.
You need to determine the focal length for your lens. To determine the focal length you can do one of the
following. (Ask for help from your TA if you cannot determine the focal length)
a) Using the lens as a magnifying glass to find the where a distant light is focused to a point.
b) Locating the image of an object which is very far from the lens (rays from that object will be
traveling parallel to the optical axis when they strike the lens). For that, you can keep the
lighted object at one end of the meter stick and the screen at the other end. Then bring the
lens very close to the screen and then move toward the object while observing the image.
(Hint: You know that parallel rays entering the converging lens go through the focal point. )
20. What is the focal length of the lens?
f = ____________________________________
Remember Units
Which of the above methods did you use? Explain how you identified the focal length.
21. Position the object a distance away from the lens that is larger than the focal length you measured
above. Start with the screen at the far end of the bench and slowly move the screen closer to the
lens. Describe what you see on the screen as you do this.
5
22. How do you know when the screen is at the location of the image?
23. Is the image the same orientation as the object (called upright) or is it inverted?
Move the object (light source) a little farther away from the lens. This makes the object distance
(distance between the object and the lens) a little larger. Now move the screen to get a sharp
image again.
24. Did you need to move the screen farther from or closer to the lens?
25. State your conclusion to this:
When the object distance is increased the image distance _______________________________________
26. Did the image get larger or smaller?
27. State your conclusion to this:
When the image distance ______________________________ then the magnification ________________________.
Please remember to write your names and attach ray tracing papers to one person’s lab report for grading.
6
Phys1112 - Electric Charge and Force
Name:
Group Members:
Date:
TA’s Name:
Objectives:
•
•
•
To become familiar with basic electric phenomena.
To learn the charge model and apply it to conductors and insulators.
To understand polarization and the attraction between neutral and charged objects.
Materials: Plastic rod, glass rod, piece of wool and silk, scotch tape, soda can, aluminum foil, Styrofoam
board, neon bulb, two aluminum pie pans, alligator clips, and electroscope.
Part A: Electrical Interactions of Sticky Tape
1. Obtain a piece of sticky tape, about 15 - 20 cm in length. For ease in handling, make "handles" by
folding each end of tape to form portions that are not sticky. Press the tape firmly onto a smooth,
unpainted surface, for example, onto a textbook or onto the table. Then quickly peel the tape off
the surface and hang it from a support.
Describe the behavior of the tape as you bring objects, such as a finger or a pen, towards it.
2. Make another piece of tape as described above. Bring the second tape toward the first tape with
the non-sticky sides facing each other. Describe your observations. It is important, that during
this experiment you keep your hands and other objects away from the tapes.
Explain why this precaution is necessary. Describe how the distance between the tapes affects the
interaction between them?
3. Press two pieces of tape onto the surface and write a B (for bottom) on them. Then press another
tape on top of each B tape and label it T (for top). Pull each pair of tapes off the surface as a unit.
After they are off the surface, separate the T and B tapes. Hang one of the T tapes and one of the B
tapes from a support. Describe the interaction between the following pairs of tape when they are
brought near one another.
Two T tapes
Two B tapes
One T and one B tape
Part B: Interactions of More Charged and Uncharged Objects
When performing the following experiments, extend the rubbed objects away from your body so that
your body does not influence your observations made with hanging tapes. Also, in humid conditions the
electric charge on the pieces of tape can “leak off” causing them to become discharged. You may have to
recharge or replace your T- and B-strips from time to time.
Create T and B tapes 15 to 20 cm long. Complete the following investigations and record your
observations.
4. Bring charged objects toward the tapes one at a time and record the observations below.
T type
Charged portion of the rod
Material
Charged area of plastic
rod, rubbed with wool
Charged area of glass
rod rubbed with silk
B type
T type tape
Attracted /Repelled/Nothing
B type tape
Attracted /Repelled/Nothing
5. You have probably heard that “like charges repel” and “unlike charges attract.” Use this fact to
explain how you can determine if any particular object is charged T type or B type.
6. From these observations, what do you conclude about the charge on the glass rod after its rubbed
with silk? What about the plastic rod rubbed with wool? Explain your reasoning then record your
conclusions below.
Glass rubbed with silk
Plastic rubbed with wool
Is the charge T or B or none?
Glass is
Plastic is
7. Now re-charge the T and B tapes or use new ones. Bring a few uncharged objects toward the
tapes. And record the observations below.
Material
Your finger
Uncharged area of
plastic rod
Uncharged area of
glass rod
paper
Aluminum foil
Wood
Cork
Metal
T type tape
Attracted /Repelled/Nothing
B type tape
Attracted /Repelled/Nothing
8. What can you conclude from your observations in Question #7? You may base your conclusions
on what you learned in the class or from the textbook?
9. Charge the plastic rod with wool. Put an empty soda can on the table (horizontal) as shown in the
figure below. Bring the charged portion of the rod parallel to the empty soda can. Do not touch the
soda can with the rod.
Observe the rolling motion of the soda can. Repeat observation with glass rod charged with silk.
Explain your observations by drawing a model for the relative charge distribution on the rod and
on the soda can for both cases. Name your charges as T or B based on your identifications in #6.
Soda can
Plastic rod
Soda can
Glass rod
10. What is the net charge of the soda can in each case? Explain the reason for your answer.
11. Can you have a net electric force on an object with no net charge? Use your observations of the
motion of the soda can to support your answer.
Part C: Charging Metals by Contact
From now on use the following information to identify charges on the plastic rod and glass rod.
Plastic rod rubbed with wool is negatively charged. (plastic negative)
Glass rod rubbed with silk is positively charged. (glass positive)
Now go back to #6 and identify T and B in terms of + and –
12. Get an electroscope similar to the one drawn below. When the metal leaves have excess charge
they repel as shown, when there is no excess charge on leaves they hang vertically down.
Metal sphere
Metal post
Metal leaves
First touch the metal sphere once with
your finger. Then bring the charged
plastic rod rubbed with wool toward the
metal sphere of the electroscope and
observe the behavior of the leaves. Do
not touch the metal sphere with the
plastic rod.
Record what you observe when you bring the plastic rod near.
What is your model of what is going on that can explain this observation?
13. Draw + and – charges on the diagram to
represent the distribution of charge on the
rod and the electroscope when the rod is
brought close to the electroscope.
14. Describe what you observe when you take the charged rod away from the electroscope.
Explain what you think is causing that behavior.
15. Now repeat #12 but instead use the charged glass rod
rubbed with silk. Describe what you see.
Compare what you see in this case to what you
observed in Question #12 for the rubbed silk.
Use + and – symbols to draw the distribution of charges on the electroscope.
Draw your conclusion for what the charge distribution and explain why you observe what you
observe.
16. Recharge the plastic rod, then touch the metal sphere
with the charged portion of the plastic rod and take
the rod away. Describe how the leaves look like after
you complete the task.
Do you think that the electroscope now has a net charge? __________________________
Explain why or why not.
Use + and – symbols to draw the distribution of charges on the electroscope.
17. One of your classmates says that the angle between the leaves is an indication of the amount of
charge present in the electroscope. That is larger angle means more charges etc. Do you agree? If
yes, why? If not, why not?
18. Use the plastic rod to investigate this claim and decide if the angle of the leaves on the
electroscope indicates how much charge is on them. Describe your observations and conclusions.
19. Charging of a conductor by touching with a charged material is called charging by contact.
Now touch the metal sphere again with your finger. Explain what happens when you touch the
metal sphere with the finger.
Electric Field
Name:
Group Members:
Date:
TA’s Name:
Simulation link: https://phet.colorado.edu/en/simulation/charges-and-fields
Type “Charges and Fields –PHET” in Google and click the link.
Objectives:
1. To understand the magnitude and direction of the electric field produced by a point charge at different
directions and distances around the point charge.
2. To understand the magnitude and direction of the electric field produced by a dipole at different
directions and distances around the dipole.
Before you begin: Your TA has set up a demonstration using two charged electrodes, a pan of water, and an electric
field sensor. This sensor has LEDs (light emitting diodes) whose brightness is proportional to the electric field
component in the direction that the sensor is pointing. Take a few minutes to move the sensor around and observe how
the magnitude and direction of the electric field depends on location. In this lab you will be using a simulation where
electric field sensors operate in a similar fashion.
Part 1: Electric Field from One Point Charge
1. The strength of the electric field around a positive point charge Q at a distance r from the center of the charge is
1 𝑄𝑄
. The direction of the electric field vector is radially outward. Sketch E
given by the equation 𝐸𝐸 =
4𝜋𝜋𝜖𝜖0 𝑟𝑟 2
vs. r graph for a positive charge. Label the horizontal and vertical axes of the graph.
1
2. Now open the simulation. Click on “Grid” and “Values” to select those options. Place a 1 nC positive (red color)
charge on the grid. This is sometimes called a “source charge” since it’s the source of the electric field we are
going to measure. To make a measurement of electric field, grab an E-field sensor and place it where you want
to measure the electric field. The arrow of the sensor indicates the direction of the E-field at that point and the
length of the arrow is proportional to the strength of the electric field.
Move the sensor around and observe how the electric field is different in magnitude and direction at different
locations. Summarize what you observe about how the magnitude of the electric depends on location.
Summarize what you observe about how the direction of the electric field depends on location.
3. Make a measurement of the electric field at 1.0 m away from the charge (scale is shown at bottom of the
screen). Note that the units of electric field are V/m = N/C. Record the value below.
E = ___________________________________
4. Predict what the strength of the electric field will be at the same point if you double the amount of charge?
E = ___________________________________
5. Place another 1 nC positive charge on top of the previous charge and measure the electric field again at the
same place. Record your result below and put back the added charge in the charge bucket.
E = ___________________________________
6. Did your prediction agree? What can you conclude about the dependence of electric field on the amount of
charge?
2
7. Now we want to investigate how the strength of the electric field depends on distance from the 1 nC positive
charge. Make measurements of the magnitude of the electric field at different r values and complete the
following table, where r is the distance measured in meters.
r(m)
0.50
1.00
1.50
2.00
2.50
E (N/C)
8. Plot the electric field vs. r graph in Excel. Does your graph show the behavior of the electric field with distance as
you predicted in #1, Yes or No?
9. Select a Power Law trend line to fit the data and display the equation. Does your power law fitting give the same
dependence of the electric field with distance as you described in #1, Yes or No?
10. Find the equation of the trend line from Excel and record it below. Also copy your Excel graph into your Word
document.
Power Law Equation: ____________________________________________________
Now rearrange this equation to be in the same form as the theoretical equation and re-write it in the box.
Electric field around a point
charge(Theoretical)
𝐸𝐸 =
Electric field around a point charge
(experimental)
𝑄𝑄 1
4𝜋𝜋𝜖𝜖0 𝑟𝑟 2
Compare the equation you obtained with the theoretical equation of electric field around point charge. From
your comparison calculate your experimental determination of the electrostatic constant, k.
𝑘𝑘 =
1
=
4𝜋𝜋𝜖𝜖0
11. Remove the positive charge and place a 1 nC negative (blue color) charge at the same place. What is different
and what is the same about the electric field due to 1 nC negative charge compared with 1 nC positive electric
charge?
3
Part 2: Electric Field from an Electric Dipole
Since atoms in a molecule often carry a net charge, many molecules are permanent electric dipoles. The figures
below shows a carbon monoxide molecule, CO, and a water molecule, 𝐻𝐻2 𝑂𝑂. A dipole is characterized by the
dipole moment with a magnitude of 𝑝𝑝 = 𝑞𝑞𝑞𝑞 , where 𝑝𝑝 is the charge and 𝑠𝑠 is the distance between the charges.
The direction of the dipole moment is defined from negative charge to positive as shown. The units of dipole
moment are units of charge multiplied by units of distance, such as Cm.
Direction of the dipole moment
+q
C
+q
s
𝑝𝑝 = 𝑞𝑞𝑞𝑞
-q
O
dipole moment
-q
of the carbon monoxide molecule
Direction of the dipole moment
+e
H
O -2e
+e
H
+2e
-2e
s
dipole moment
𝑝𝑝 = 2𝑒𝑒𝑒𝑒
of the water molecule
12. Now we will examine the electric field of a dipole. The magnitude and direction of the electric field depends on
the distance and the direction. We will investigate in detail just two directions. With charges available in the
simulation how do you create a dipole with dipole moment 1 x 10-9 Cm with a direction for the dipole moment
pointing to the right? Look back at the figure at the top of the page to make sure you determined the direction
of the dipole moment correctly. Make a sketch below that shows the amounts of charge and the distance
between the charges. There are many correct answers.
13. On your drawing in #12, mark the center of the dipole as the origin (x=0, y=0). Pick a point to the right of the
charges and mark it as P1. At that point draw vectors to represent the electric field contributions from each of
the individual charges in your dipole. Each electric field vector should be drawn with its tail at point P1. Also
draw a vector to represent the net electric field produced by all the charges in the dipole. Label that vector
as 𝐸𝐸�⃗𝑛𝑛𝑛𝑛𝑛𝑛 .
4
14. Now reproduce the dipole on the grid in the simulation making sure that the dipole moment is directed to the
right and the magnitude of the dipole moment is 1 x 10-9 Cm. We’ll make the center of the dipole to be our
origin (x=0 m, y=0 m) on the grid.
15. Make measurements of 𝐸𝐸�⃗ at a series of points along the x-axis to the right of the dipole and record its
magnitude and direction at each position.
x(m)
1.0
1.5
2.0
2.5
3.0
y (m)
0.0
0.0
0.0
0.0
0.0
E(N/C)
Direction
16. Plot the measured dipole electric field strength vs. r graph in Excel. Which electric filed (single charge or dipole)
drops off more with distance? Use the electric field graphs to support and explain your answer.
17. Make some measurements of 𝐸𝐸�⃗ at points along the x-axis to the left of the dipole. How do the magnitude and
direction of the electric field on the left side of the dipole compare to the right side for the same distance?
18. On your drawing in #12, pick a point above the center of the dipole and mark it as P2. At that point draw vectors
to represent the electric field contributions from each of the individual charges in your dipole. Each electric field
vector should be drawn with its tail at point P2. Also draw a vector to represent the net electric field produced by
all the charges in the dipole. Label that vector as 𝐸𝐸�⃗𝑛𝑛𝑛𝑛𝑛𝑛 .
5
19. Make measurements of 𝐸𝐸�⃗ at a series of points along the y-axis above the dipole and record its magnitude and
direction at each position.
x(m)
0.0
0.0
0.0
0.0
0.0
y (m)
0.5
1.0
1.5
2.0
2.5
E (N/C)
Direction
20. Make some measurements of 𝐸𝐸�⃗ at points along the y-axis below the dipole. How do the magnitude and
direction of the electric field above the dipole compare to below the dipole?
Part 3: Conclusions
21. Summarize what you observed about the magnitude and direction of the electric field from a single point
charge. In particular, how does the electric field depend on distance from the point charge?
22. Summarize what you observed about the magnitude and direction of the electric field from a dipole. In
particular, how does it depend on distance and direction from the center of the dipole?
Instructions on how to submit the graphs:
1. Open a word document and type the names of all present group members.
2. Copy your Excel graphs (with title and axis labels) to your Word document.
3. Print the document (one for each group) and attach it to the lab write-up for one member of the group.
6
Name:
Phys1112 - Parallel Plate Capacitor
Objectives
1. To understand the characteristics of a parallel plate capacitor.
2. To understand the relationship between plate area, plate separation, and capacitance.
3. To understand the relationship between charge, voltage, electric field, and capacitance.
Simulation link: https://phet.colorado.edu/en/simulation/capacitor-lab-basics
Upon launching, the simulation should look like this.
Notice that the capacitor shown is made of two conductors that are separated. In this case, two square
plates. The only physical characteristics are the plate area and the plate separation.
Part A: Relationship of Charge and Voltage for Parallel Plates
1) Using the default separation and plate area, adjust the battery to 1.5 V. What happens when you
apply a voltage across the capacitor?
2) How does the charge on the top plate compare with the charge on the bottom plate?
3) What do you think the total charge is, that is, the charge on the top plate plus the charge on the
bottom plate?
4) Adjust the battery to different values between 0.0 V and 1.5 V. What effect does changing the
voltage across the capacitor have on the charge of each plate?
5) Now adjust the battery to different values between 0.0 V and -1.5 V. How does this situation
compare with the previous one?
6) Set the battery to a value between 0.0 V and 1.5 V. Now drag the voltage meter toward the
capacitor and move the red and black leads to measure the voltage. Determine the potential
difference between the two plates and whether the top plate is at higher or lower voltage than the
bottom plate.
∆𝑉𝑉 = 𝑉𝑉𝑡𝑡𝑡𝑡𝑡𝑡 − 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = ________________________
Is top plate at higher or lower potential than the bottom plate? Explain.
7) Click the box labeled “Top Plate Charge.” Change the voltage to six different values between -1.5 V
and 1.5 V choosing three positive values and three negative values. For each voltage, also
determine the charge on the top plate. Note: make sure you get the sign correct, red is for positive
values of the charge and blue is for negative values.
Top Plate Charge, Q (pC)
Voltage, 𝛥𝛥V (V)
8) Use Excel to plot Q vs. 𝛥𝛥V. Fit an appropriate equation to the data and display the equation on the
graph. Label the graph appropriately and copy and paste it into this Word document.
Describe the relationship between the charge on each plate of the capacitor and the potential
difference across the capacitor.
9) Notice that we didn’t change the physical characteristics of the capacitor in this experiment, just
the voltage we applied to it. The physical characteristics (plate area and separation) determine
the capacity of the device to hold a charge on each plate at any particular voltage, a property called
capacitance. How does the value you determined for the slope Q vs. 𝛥𝛥V compare to the value given
in the simulation for the capacitance?
10)Adjust the battery to different values between -1.5 V and 1.5 V. Does the value given in the
simulation for the capacitance change as you change the voltage?
11)Does the capacitance depend of the voltage applied to the capacitor? What do you think it depends
on?
Part B: Changing the Dimensions of the Parallel Plates
12)Now we’re going to investigate what happens when we change the dimensions of our capacitor.
Set the battery voltage to zero so there is no charge on the capacitor, then disconnect all meters
and the battery from the capacitor. Keep the plate separation constant at 6.0 mm while you vary
the area of the plates. Take some data to determine the capacitance, C, for five different values of
Plate Area, A.
Plate Area, A (mm2)
Capacitance, C (pF)
13) Determine how capacitance, C, depends on plate area, A. Explain what you concluded and how
you determined it.
14)Now set the Plate Area to 200 mm2 vary the separation of the plates. Take some data to determine
the capacitance, C, for five different values of Plate Separation, d.
Plate Separation, d (mm)
Capacitance, C (pF)
15) Determine how capacitance, C, depends on plate separation, d. Explain what you concluded and
how you determined it.
16) Write an equation that shows the relationship of capacitance to both plate area and separation.
It’s only the physical parameters that determine capacitance, so neither charge nor voltage should
be in this equation. It tells us how the capacitance depends on the parameters we use when we
construct the capacitor. Since the earlier experiments you determined the relationships, this
equation will require at least one constant, so just use the word constant or k in your equation.
Part C: Electric Field in a Parallel Plate Capacitor
In Part A we saw how the capacitance tells us how much charge will be on each plate for a given voltage.
In Part B we saw how the physical parameters determine the capacitance. In most cases, a capacitor is
built with a given plate area and separation that determines the capacitance. The value of the capacitance
is even stamped right on the side of the device in most cases. However, in this simulation we can vary the
construction to get a better idea of why the charge and voltage have this relationship.
17) Reconnect the battery, attach the voltmeter, and adjust to 0.25 V. Check the box marked Electric
Field. Notice the pattern of electric field lines. What direction do they point? Are they straight or
curved? Are they closer together in some places? Explain what the pattern of electric fields lines
tells us.
18) Increase the voltage to 0.50 V. What happens to the magnitude and direction of the electric field
between the plates? Explain how the voltage and electric field are related to each other.
19) What did the battery actually do to achieve the new voltage setting? Look at the amount of charge
on the plates and watch the simulation carefully for a clue while you change the voltage. What
effect did the change in charge have on the electric field.
Part D: Putting it all together
20) Complete the following table to summarize the relationships of the parameters by writing
increase, decrease or same in the empty boxes. To accomplish the last two lines, you will need
to put some charge on the capacitor and then disconnect it from the battery. The capacitor
will stay charged when you do that because the charge has nowhere to go. Also, check the box at
the top labeled “Stored Energy” and record the changes to that quantity.
Plate
Separation
increase
Plate
Area
same
same
increase
increase
same
same
same
same
Capacitance
Voltage
same
same
increase
increase
Explain each line of the table. What happened and why?
Top Plate
Charge
same
same
Electric
Field
Stored Energy
Name:
Phys1112: Electric Potential Energy and Electric Potential
Group Members:
Date:
TA’s Name:
Objectives
1. To understand the electric potential of a point charge.
2. To understand the electric potential of a dipole.
Simulation link: https://phet.colorado.edu/en/simulations/charges-and-fields
or Type “Charges and Fields –PHET” in Google and click the link.
Part 1: Electric field and potential of a point charge
In a previous experiment we investigated the electric field of a point charge and a dipole. Electric field is
produced by source charges and is present everywhere in space. The electric field created by one charged
object will exert forces on other charged objects in that same region. The strength and direction of the
electric field at a given point in space can be measured by measuring the electric force acting on a unit
positive test charge. If the electric field due to a source charge or charge distribution is known then one
can find the electric force on a charge 𝑞𝑞 in the field by using the equation: ����⃗
𝐹𝐹𝐸𝐸 (𝑥𝑥, 𝑦𝑦, 𝑧𝑧) = 𝑞𝑞𝐸𝐸�⃗ (𝑥𝑥, 𝑦𝑦, 𝑧𝑧).
So far we have studied electrical interaction in terms of electric force concepts. In this lab we are going to
take a look at a system of charges with a different perspective. We want to study a system of charges in
terms of its electrical interaction energy or the electrical potential energy, Uelec. For that purpose we
define a quantity called electric potential, V. Electric potential is defined as the electric potential energy
per unit charge. Once we know the electric potential at some location, we can use it to find the electrical
potential energy of charges placed at that location. This should remind you of the way we calculate
electric force on a point charge in an electric field. Electric potential energy and electric potential are
related by the equation: 𝑈𝑈𝑒𝑒𝑒𝑒𝑒𝑒𝑐𝑐 = 𝑞𝑞𝑞𝑞. Here 𝑉𝑉 is the electric potential (created by whatever source
charges there are) at the location in space which the object with charge q is located. Since energy is a
scalar quantity, then 𝑉𝑉 is also a scalar quantity. In future experiments you will find that one use of
electric potential is for analyzing electrical circuits.
1. What is the unit of electric potential? Use the units for potential energy and charge to find express
it in terms of other units.
2. Open up the electric field simulation, turn on the Grid and Show Numbers, and place a positive
point charge of +1 nC at the center of the grid. Make measurements of electric potential and the
magnitude of the electric field at the following points to the right of the point charge. Use the
voltmeter to measure electric potential. The meter measures the electric potential at the point
where the center of the cross is located. Be sure to put the units for E and V.
Distance, r(m)
0.5
Magnitude of Electric Field, E
Electric Potential, V
1.0
1.5
2.0
2.5
3.0
3. What creates the electric field and electric potential you measured?
4. Does the electric potential around the point charge decrease or increase with increasing distance?
5. Equipotential lines are lines with equal electric potential (for example, all the points with an
electric potential of 5.0 V). Using the plot tool that comes with voltmeter make two equipotential
lines at 𝑟𝑟 = 0.5 𝑚𝑚 and 𝑟𝑟 = 1.5 𝑚𝑚. Enable electric field vectors in the simulation. Put an electric
field sensor at different points on the equipotential line and note the direction of the electric field
vector. What can you conclude about the direction of the electric field vector in relation to the
equipotential lines?
6. Use the electric field sensor to investigate points in between the two equipotential lines. Does the
electric field vector point toward the higher electric potential, toward lower electric potential, or
along an equipotential line?
7. Using your data from Question #2, plot electric potential vs. r in Excel. This is called the “Potential
Graph.”
8. One of the students in the class says that the electric potential at locations around a source charge
is inversely proportional to the distance from the source charge to that location. Use your data to
test this hypothesis. Explain what you did to test the hypothesis, the result of the test, and your
conclusion.
Ask your TA to check your result before going on. TA initials ___________________________
Part 2: Electric force and potential energy for two charges
9. Assume that you are going to bring another +1 nC charge to the locations where you measured
electric field and potential from the first +1 nC charge in Question #2. Copy the values (with units)
for E and V you found in Question #2. Then calculate the magnitude of the electric force on the
second charge, the direction of the force, and the electrical potential energy of the system. Refer
back to the first page if you aren’t sure how to calculate FE or Uelec.
r(m)
0.5
1.0
1.5
2.0
2.5
3.0
E
V
FE (N)
Force Direction
Uelec (J)
10. Using the ideas of electric field and force, explain what would happen to a proton if released from
rest at 𝑟𝑟 = 1.5 𝑚𝑚. (simulation does not show this).
11. Would the proton released from rest move to a region of higher electrical potential or lower
electrical potential?
12. Would the proton released from rest move such that the system would have higher potential
energy or lower potential energy?
13. Now we will investigate the force, energy, and potential when a negative charge is placed in the
field created by the first positive charge. Assume that instead of using a second positive charge,
you brought a -1 nC charge to each of the locations where you measured electric field and
potential from the +1 nC source charge in Question #2. Again copy the values (with units) for E
and V you found in Question #2. Then calculate the magnitude of the electric force on the second
charge, the direction of the force, and the electrical potential energy of the system. Again refer
back to the first page if you aren’t sure how to calculate F or U.
r(m)
0.5
1.0
1.5
2.0
2.5
3.0
E
V
Force (N)
Force Direction
Uelec (J)
14. Using the ideas of electric field and force, explain what would happen to an electron if released
from rest at 𝑟𝑟 = 1.5 𝑚𝑚? (simulation does not show this).
15. Would the electron released from rest move to a region of higher electrical potential or lower
electrical potential?
16. Would the electron released from rest move such that the system would have higher potential
energy or lower potential energy?
17. Compare your answers in Questions 10 and 14. Summarize how the direction of the electric field
and the sign of the charge placed in that field determine the direction of the force.
18. Compare your answers in Questions 11 and 15. Do electric forces always push the charged object
toward a region of higher or lower electric potential? Support your answer.
19. Compare your answers in Questions 12 and 16. Electric forces are conservative forces. Do electric
forces always push the system toward higher or lower potential energy? Support your answer.
Part 3: Conclusions
20. Summarize the relationship of electric field to electric force.
21. Summarize the relationship between electric field vectors and equipotential lines.
Phys1112K:
Current, Resistance and Voltage in Circuits
Name:
Group Members:
Date:
TA’s Name:
Apparatus: Bulb board with batteries, connecting wires, two identical bulbs and a different bulb, a digital
multimeter with leads.
Objectives:
1. To be familiar with the current and voltages across different circuit elements in a series circuit
2. To be familiar with the currents and voltage across circuit elements in a parallel circuit
3. To develop intuition about the electrical power dissipation across a resistor
4. To experimentally obtain Kirchhoff’s laws used for circuit analysis
Current (I) is the amount of positive charge flowing across the cross section of the wire (conductor) per
second and measured in amperes (A).
Part A: Series circuit
1.
Set up the circuit shown with one of two identical bulbs
(look for the same type of bulbs; Ex: spherical ones).
Then change the circuit to use the other of the two identical
bulbs. Is the brightness of the two bulbs about the same?
-
++
-
++
Can you conclude that the bulbs are nearly identical?
2.
Set up the circuit shown below using the two identical
bulbs. This way of connecting bulbs to the battery is
called a series connection. Draw arrows on the figure
to indicate the direction you believe that the current is
flowing in the circuit.
Are the two bulbs brighter, dimmer, or the same
brightness as the one bulb circuit in Question 1?
3.
C
A
B
For the two bulb circuit in Question 2, how do the two bulbs compare in brightness to each other?
4.
What can you conclude about the current flow at different points in the circuit from your
observations of the brightness of the two bulbs in series?
1
5.
If you were to connect an ammeter to measure current in the circuit at points A, B, and C how
would the readings compare? (Do not connect ammeter yet) Explain the reasoning for your prediction.
6.
A digital multimeter can be used as an ammeter to measure currents. Select the proper terminals
to measure currents and choose appropriate range. Remember that an ammeter must be connected in
series since it measures the current passing through the meter itself. Ask the TA for help if needed. Then
connect the ammeter at point A between the negative terminal of the battery and the bulb (left bulb in
the drawing). Measure current at A and enter it below. Then measure currents at B and C also.
IA
IB
IC
7.
Do the measurements agree with your prediction in Question 5? If not, explain what went wrong
with your initial reasoning.
8.
Now set up the circuit shown below using the two different types of light bulbs (for example one
spherical and one cylindrical).
-
+
C
A
How do the two bulbs compare in brightness?
B
9.
Measure the current at the three points (A, B, and C).
IA
IB
IC
2
10.
How do the values of the current compare at these three points? Why? Think about the definition
of the current to answer this question.
11.
If the bulbs are different in brightness, what do you think causes that to be the case? (Just write
what you think, no points are deducted here)?
There is a property of circuit elements called resistance, which is the opposition a circuit element offers
to the flow of charge through it. Identical bulbs would have identical resistances and different bulbs will
have different resistances.
12.
Disconnect the bulbs from the circuit and measure the resistance of each bulb using the digital
multimeter. If needed, your TA will demonstrate how to use digital multimeter as an ohmmeter that
measures resistance. Then measure the total resistance when they are connected together in series. The
unit of resistance is Ohms (Ω).
Resistance of
Bulb 1
Resistance of
Bulb2
Total Resistance when
connected in series
13.
Is the resistance higher or lower for the bulb that was brighter compared with the bulb that was
dimmer (Question 8)? What do you conclude about how resistance is related to the brightness of each
bulb for the same current in a series circuit?
3
14.
The digital multimeter can also be used as a voltmeter which
measures the potential difference across a circuit element like a
light bulb or a battery. Connect the voltmeter ACROSS the battery
holder by connecting one lead from the voltmeter to one side of the
battery pack and the other lead from the voltmeter to the other side of
the battery pack (the voltmeter is in parallel connection to the battery).
If you are using the lab power supply, then connect the positive
terminal (red) to positive of the multimeter and negative terminal to the
negative (common-black) of the multimeter.
A
Record the voltmeter reading (remember units)
15.
16.
+
ΔVbattery = __________________
Predict: If you connect the voltmeter ACROSS each bulb would you expect
A. the readings to be equal to each other?
B
C
Voltmeter
B. both readings to be equal to battery or power supply voltage?
C. another result such as _______________________________________________
Now connect the voltmeter across each of the two bulbs in the circuit and measure voltages across
each bulb. Enter the results in the table below.
ΔVB1
ΔVB2
ΔVbattery
17.
How do the voltages across the two bulbs compare with each other? Re-draw the circuit showing
the current through each element and the voltages across each element obtained from measurements.
18.
Based on your measurements of potential differences (voltage) across the bulbs (𝛥𝛥𝛥𝛥𝐵𝐵1 𝑎𝑎𝑎𝑎𝑎𝑎 𝛥𝛥𝑉𝑉𝐵𝐵2 )
and the battery voltage 𝛥𝛥𝛥𝛥𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 write down an equation relating 𝛥𝛥𝛥𝛥𝐵𝐵1 , 𝛥𝛥𝛥𝛥𝐵𝐵2 𝑎𝑎𝑎𝑎𝑎𝑎 𝛥𝛥𝛥𝛥𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 for the
series circuit. This is the Kirchhoff’s loop law applied to the series circuit you studied.
4
Part B: Parallel circuit
C
19. If you were to construct the circuit shown (this is called
a parallel connection) using two identical bulbs how
do you think the bulbs will compare in brightness? Explain.
B
A
+
20. Now set up the circuit and check your prediction regarding brightness of bulbs. What did you find?
21. Prediction: If you were to measure the current at points A, B and C, how do you think the values
would compare? Why?
22. Prediction: If you were to measure the potential differences across these bulbs (what the voltmeter
measures) how do you think the values will compare to each other and to the potential difference
across the battery pack or the power supply? Why?
5
23. After discussing these predictions with your group members, make the appropriate measurements
with your digital multimeter (the ammeter and voltmeter). Make sure you connect the ammeter and
voltmeter properly (one is always connected in series and one is always connected in parallel)!
Remember units.
IA
IB
IC
ΔVB1
ΔVB2
ΔVbattery
24. Re-draw the circuit showing current and voltages across each element obtained from measurements.
25. Based on your current measurements write down an equation relating currents 𝐼𝐼𝐴𝐴 , 𝐼𝐼𝐵𝐵 𝑎𝑎𝑎𝑎𝑎𝑎 𝐼𝐼𝐶𝐶 . This is
the Kirchhoff’s junction rule applied to a junction in the parallel circuit you studied.
26. You already know the resistance of each bulb and they are the same. Disconnect the power supply or
batteries and measure the total resistance of the parallel circuit. Enter the results in the table below.
Resistance of
Bulb 1
Resistance of
Bulb2
Total Resistance when
connected in parallel
You may increase or decrease the total resistance of a circuit by adding resistances to a circuit. Total
resistance depends on how you add resistors to the circuit. Fill in the blanks below based on your data
from #12 and #26 above.
•
•
Arranging resistances in series ________________________ total resistance in the circuit.
Arranging resistances in parallel ______________________ total resistance in the circuit.
6
Phys1112: DC and RC circuits
Name:
Group Members:
Date:
TA’s Name:
Objectives:
1.
2.
To understand current and voltage characteristics of a DC RC discharging circuit.
To understand the effect of the RC time constant.
Apparatus:
PASCO voltage-current sensor, power supply (10V), two alligator clips to connect the capacitor, five long
banana wires, 25000 µF bipolar capacitor, 100 Ω and 250 Ω resistor, PASCO interface with PASCO
software, multimeter.
Bipolar capacitor: Correct functioning of the bipolar capacitor requires connecting higher potential to the
positive (red) terminal of the capacitor and lower potential to the negative terminal of the capacitor.
Part A: RC circuit - Discharging a capacitor
In the previous experiment we measured currents and voltages in a series and parallel circuit involving
resistors (light bulbs). In a circuit with only resistors and batteries, the current through and voltage
across each resistor do not change with time. However, if the circuit involves a capacitor, then the
current and voltage across circuit elements do change with time. In this experiment we investigate
current and voltage in a series circuit involving a resistor and a capacitor referred to as an 𝑅𝑅𝑅𝑅 circuit.
1.
The amount of charge that must be moved from one side of the capacitor to the other to establish a
voltage, V, for a capacitor with capacitance, C, is given by
. Calculate the amount of charge that
will be moved from one side of the capacitor to the other if we hook a 10 V battery up to the 25000 μF
capacitor. Show your work and pay attention to units.
Q = ___________________________________________
2.
The capacitor is charged to 10 V and then connected to a 100 Ω resistor
in the circuit shown to the right. If the voltage across the capacitor is 10 V,
voltage will be across the resistor right after the circuit is connected?
VR = _____________________________
+Q
-Q
RC circuit
The loop rule for circuits may be useful here. The total change in voltage (or the total potential
difference) must be zero whenever we go around a closed loop.
1
3.
Using the voltage across the resistor, calculate the amount of current that must be flowing through
the resistor (and in the rest of this single loop circuit) immediately after we connect the circuit as shown.
Remember that the voltage across the resistor is given by ∆VR=IR. Show your work.
+Q
-Q
I = __________________________________________
Draw arrows on the figure to the right to show the direction
that the current is flowing.
4.
Current is the rate at which charge is flowing. As the current flows in the direction you indicated,
will the amount of charge on the left plate of the capacitor increase, decrease, or stay the same? Explain.
5.
As the current flows in the direction you indicated, will the amount of charge on the right plate of
the capacitor increase, decrease, or stay the same? Explain.
6.
So as the current flows in the direction you indicated, will the voltage across the capacitor
increase, decrease, or stay the same? Explain.
7.
Using what you determined about the change in the voltage across the capacitor, will the voltage
across the resistor increase, decrease, or stay the same? Explain.
8.
Using what you determined about the change in the voltage across the resistor, will the current
flowing in the circuit increase, decrease, or stay the same? Explain.
Check your answers with your TA before you proceed. TA initials ____________________
2
9.
Since current is the rate at which charge is flowing, if the current in the circuit decreases, what
does that mean about the rate at which the charge (and voltage) on the capacitor changes?
10.
Sketch your predictions for the graphs of voltage across the resistor versus time and current in the
circuit versus time for the RC circuit.
I
∆VR
t
t
Part B: Discharging a capacitor - Voltage vs. time and current vs. time
Now we will make the following circuit, charge the bipolar capacitor to 10V, and then investigate voltage
and current in the discharging. Do not connect the circuit to the power supply yet. Wait for TA’s
approval before you do that. Use a 100 Ω resistor and blue cylindrical 25000 μF bi-polar capacitor (note
+ and – signs). You will be using PASCO voltage–current sensor to measure voltage and current across
the resistor and capacitor. Select the data sampling frequency to be 5 Hz that means the sensor collects
voltage and current data 5 times per second.
Ammeter
10V
25000μF
R
V
Voltmeter
Have your TA check your circuit set up before continuing. TA initials _______________________
3
100Ω
Once the circuit is connected, open Capstone software and click on the two-graph template. Choose the
vertical axis to be voltage in one graph. Choose current to be the vertical axis in the other graph. Both
should have horizontal axis as time. If the vertical axis does not show voltage/current options that means
either the sensor is faulty or there is not a good connection to the interface.
Now connect the power supply and charge the capacitor. (In the picture, black wire would be connected
to the negative terminal of the power supply).
Start recording data while the power supply is connected and then disconnect the power supply. Record
data for about 10-12 seconds and stop recording. You should have a nice voltage vs. time graph and a
current vs. time graph. If necessary practice doing this several times until you are satisfied with the
graph. Keep the best run and delete the others.
11.
Sketch the curves you measured below. For the sketches, make t=0 the time when you
disconnected the power supply.
I
∆VR
t
4
t
12.
How does the shape of the measured voltage vs. time and current vs. time graphs compare with
your predictions in Question 10?
13.
How would you describe the slope of each curve and how they are changing as time increases?
As you might have guessed from the shape of the current and voltage curves, the discharge process
follows an exponential decay curve. The voltage across the capacitor (∆𝑉𝑉𝐶𝐶 ) at time 𝑡𝑡 is expected to be
given by ∆𝑉𝑉𝐶𝐶 = ∆𝑉𝑉0𝑒𝑒 −𝑡𝑡/𝑅𝑅𝑅𝑅 , where ∆𝑉𝑉0 is the initial voltage of the capacitor at 𝑡𝑡 = 0. Since ∆𝑉𝑉0 is the
voltage at one specific time, it is a constant in this equation. So the only variable on the right side of the
equation is t.
14.
The exponent of the exponential function contains 𝑅𝑅𝑅𝑅 for the given circuit, which is called the time
constant. Use the units of 𝑅𝑅 and 𝐶𝐶 to find units of 𝑅𝑅𝑅𝑅. Write ohms in terms of volts and amps and write
farads in terms of volts and coulombs. Simplify until you get something simple. Show your work below.
Units of RC are _______________________________________________________
Are these units consistent with the name “time constant”?
Part C: Determining the effect of changing the resistance
15.
If we used a larger resistor in the circuit, would the current be larger, smaller, or the same just
after we disconnect the power supply?
16.
Based on your answer to Question 15, do you predict that the discharge of the capacitor will be
faster, slower, or the same if we use a larger resistor? Explain why.
5
17.
Now with the power supply disconnected, change the resistance to 250 Ω. Follow the steps above
to collect and get the current and voltage graphs for the discharge of the capacitor. Display both voltage
vs. time curves (100 Ω and 250 Ω) on the same graph. Also display both current versus time curves on
one graph. Selecting both runs from the ‘third item from the left of Graph menu’ can do this.
Sketch the curves you measured for both the 100 Ω and the 250 Ω resistor below. For each sketch, adjust
the curve so that t=0 is the time that you disconnected the power supply. Make sure you are accurate
about whether the two voltages curves start at the same value. Also make sure you are accurate for the
current curves. Make sure and indicate which curve is for 100 Ω and which is for 250 Ω.
I
∆VR
t
t
18.
Is the discharge faster, slower or the same with 250 Ω as it was with 100 Ω? Does this match your
prediction? If not, explain why it behaves different than you thought it would.
19.
Is the initial current larger, smaller or the same with 250 Ω as it was with 100 Ω? Does this match
your prediction? If not, explain why it behaves different than you thought it would.
6
Part D: Conclusions
20.
Would the capacitor discharge more quickly or more slowly if we had used a capacitor with a
smaller value of capacitance? Explain.
21.
Why does the capacitor charge almost instantly when the power supply is connected?
22.
Why does the capacitor discharge more slowly when the switch is opened compared to charging?
7
Phys1112 - Magnetic Fields
Name:
Group Members:
Date:
TA’s Name:
Objectives:
To measure and understand the magnetic field of a bar magnet.
To measure and understand the magnetic field of an electromagnet, in particular, a solenoid.
Apparatus:
Bar magnet box, compass, PASCO magnetic field sensor, PASCO interface, multimeter, red and black
leads, rheostat.
Electric charges produce electric fields. Magnets and electromagnets produce magnetic fields. We used
the electric field model to explain how a charge or a charge distribution exerts forces on other charges at
a distance. Similarly we use the magnetic field model to explain how a magnet exerts forces on other
magnets and charges moving relative to the field. Therefore magnetic field is a vector quantity. Magnetic
field is measured in Tesla (T). “Tesla” is a large unit with one Tesla being a very strong magnetic field.
Small magnetic fields like the magnetic field of a small bar magnet are measured in millitesla. The
horizontal component of the earth magnetic field is about 50 microtesla on the surface of the earth.
We learned that positive and negative electric charges can be separated and monopoles and dipoles occur
naturally. However, in magnets we only find magnetic dipoles in nature where we always find a “north
pole” and “south pole” together.
Here in this experiment we qualitatively investigate the magnetic field around a bar magnet (permanent
magnet) and an electromagnet using a tiny test magnet called a “compass”. Then we will measure the
magnetic field of a bar magnet and an electromagnet using PASCO magnetic field sensor and study how
the magnetic field depends on position, current, etc.
Part A: Permanent Magnets
1. Take the two bar magnets out of the box and investigate their interaction. Explain how the poles
interact in terms of attraction and repulsion.
2. Now place one magnet on the marked space below and identify north and south poles of the
magnet. The direction of the magnetic field at a point in space is indicated by the compass magnet.
Then using the compass identify the direction of the magnetic field at the points shown. Then
draw magnetic field lines connecting appropriate points to create a magnetic field line drawing.
3. Now connect the PASCO magnetic field sensor to the PASCO passport interface and the interface
to the computer via USB cable. Open up the CAPSTONE software and select the graph and meter
window. Select the vertical axis to be “magnetic field” and the horizontal axis to be “time.” Change
the sampling rate to 10 samples per second. Press the record button and see if it records data on
the graph. Move the sensor away from magnets and see if the value changes from position to
position and in which direction the sensor is directed. Enlarge the scale of the magnetic field axis
to read the value in minitesla. (1 mT = 0.001 T).
Align the sensor as follows to measure the magnetic field.
Direction of the magnetic field
When you align the sensor as shown
Reading is positive.
The sensor has to be perfectly aligned with the magnetic field to measure it accurately. Make sure
that you keep the sensor as shown in the figure.
4. Keep the magnetic field sensor as shown below and measure the magnetic field at the edge of the
magnet. It may be helpful to put something under the magnet so that the magnet and sensor are at
the same height. Then move the sensor along the axis of the magnet to the right and measure the
magnetic field at five different points. Keep the sensor at a fixed position and run the program to
see the reading as a function of time. Get the average reading and record it below.
Magnet
S
Sensor
N
Position (cm)
Magnetic field strength (mT)
0.1
0.5
1.0
1.5
2.0
2.5
5. Transfer data to an Excel file and plot magnetic field vs. position. Draw an appropriate trend line
and display the equation on the chart. Name the graph, label axes, and display units.
Show the graph to your TA and get this space initialed ___________________________
6. Qualitatively explain how the strength of the magnetic field changes with distance from the edge
of the magnet based on your graph.
7. Your data might indicate a magnetic field even when the sensor is far away from the magnet. What
are the possible reasons for this situation? (Slowly move the probe around other wires, computers
etc. and see if they indicate any magnetic field)
Part B: Electromagnets
The figure below shows a schematic diagram of a solenoid. The direction of the magnetic field
created by the solenoid depends on how the wire is wrapped and the direction of the current flow
(which end it enters). The strength of the magnetic field depends on the number turns per unit
length of the solenoid, the current in the wire, and the magnetic permeability in the medium.
magnetic field
N
S
current in
current out
You are given a solenoid and it is an electromagnet. Carefully observe how it is made. An insulated
wire is wrapped around a hollow metallic cylinder. When a current flows through the wire the
solenoid becomes an electromagnet. In this experiment you want to investigate the strength of
the magnetic field inside the solenoid as the current is varied.
We need to send a known current through the solenoid wire and measure magnetic field. Connect
the circuit as shown below for the experiment.
Sensor
Interface
computer
Solenoid
Power supply
Ammeter
Rheostat (variable resistor)
8. Power supply is set around 5.0V for you and adjust the rheostat until the current indicated by the
ammeter is 0.25 A. Place the magnetic sensor as shown above and make sure that aligns with the
axis of the solenoid. Insert the probe about one inch into the solenoid and read the measurement.
With trial and error find out the maximum reading for recording. Record the reading below with
units.
Magnetic field = __________________________________
9. Switch off the power supply. Then switch the direction of the current by switching the wires
connected to the power supply. Switch on the power supply. Record the reading below with units.
Make sure the current is still 0.25 A.
Magnetic field = __________________________________
10. Why does the magnetic field have a different sign now? Explain.
11. Now repeat the same measurement as in Question #8 with a range of values for the current
flowing through the wires of the solenoid. Record your data in the table.
Current (A)
Magnetic field (mT)
0.25
0.50
1.25
1.50
1.75
2.00
The magnetic field inside a solenoid is expected to be given by the equation
𝐵=
where
𝑛=
𝑁
𝐿
=
𝜇0 𝑁𝐼
𝐿
= 𝜇0 𝑛𝐼
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑢𝑟𝑛𝑠
𝐿𝑒𝑛𝑔𝑡ℎ
, 𝜇0 = 1.257 × 10−6 Tm/A
So this suggests that the magnetic field is linearly dependent on the current. Plot the magnetic
field vs. current graph in Excel. Draw a linear trend line and display equation on chart.
Show your graph to your TA and get this space initialed ___________________
12. Are your measurements of magnetic field vs. current consistent with a linear relationship?
Explain why you come to that conclusion.
13. Use the slope of your linear fitting to determine the number of turns per unit length, 𝑛, for this
solenoid. Show your work. Remember to watch exponents since you measured the field in mT.
𝑛 = ____________________________
Part C: Conclusions and Reflection
14. What are three things you learned about the magnetic field of a bar magnet? Use your data to
support the answer.
15. Summarize what you learned about the magnetic field of a solenoid.
16. We did not consider the effect of earth’s magnetic field when doing our experiment. Would your
results be effectively different if we considered the effect of earth’s magnetic field? You need to
pay attention to the earth’s magnetic field vector (magnitude and direction) when making your
arguments.