Physics 226 Lab
Lab
1
Electrostatics and Coulomb’s Law
What You Need To Know:
The Physics From lecture you should know there are 2 types of charge, positive and
negative. The elementary particle with one unit of positive charge is the proton and
the elementary particle with one unit of negative charge is the electron. Charges that
you measure will always be multiples of the fundamental unit of charge given by
these two particles. Fractional charges are only available for quarks, there are 3 of
these inside baryons which are for example protons and neutrons.
The unit of charge is the Coulomb (C), this is a large unit. The electron and proton
charges and masses are given in the chart below.
Electron (e)
me = 9.1 x 10‐31 kg
e = ‐ 1.602 x 10‐19 C
Proton (p)
mp = 1.67 x10-27 kg
e+ = 1.602 x 10-19 C
When we charge or discharge on object we are talking only of the motion of electrons.
A lack of electrons leaves a positive charge, too many electrons makes the charge
negative. Today you will be charging objects by conduction (direct contact: rubbing
with several different materials, removes electrons or leave extra ones behind.) and
induction (no contact: bringing a charged object close to an uncharged one and
thereby making electrons move around on the uncharged object).
FIGURE 1 −
Symbol for
Ground
Another important concept is that of GROUND. When you ground an object we use
the symbol shown in Figure 1. Think of the ground as an infinite source or sink of
electrons. If you want electrons present they will flow from ground to the object, if
electrons want to leave an object, electrons can flow away to ground. Luckily,
because the ground is so HUGE and is basically the entire Earth, it remains neutral.
Conduction: When you rub a piece of plastic (like a comb) with a soft cloth like your
tee shirt it becomes charged. Electrons transfer from the plastic to the cloth. You can
pick up small pieces of paper with the comb. Objects will either become positively or
negatively charged, depending on the material and what they are being rubbed with,
plastic, silk, fur or cotton have different properties. You will be investigating these.
You will be using one piece of equipment called an electroscope. This is a sealed jar
with 2 parallel gold foil leaves inside. If the 2 gold leaves become charged they will
separate, the degree of separation is an indication of the amount of charge present. A
wide separation means a BIG charge.
1-1
Electrostatics and Coulomb’s Law
Physics 226 Lab
Example of Conduction With an Electroscope
Shown in Figure 2 is an electroscope and a positively charged rod is being brought
close to it. Electrons will be attracted to the rod and move up to the metal sphere on
top of the jar. The gold leaves then are left with an overall positive charge and hence
they separate.
LEAVES
FIGURE 2 −
A charged
electroscope
CONDUCTION: If you were to touch the top metal sphere with the positive rod,
then charge would transfer from the electroscope to the rod. When electrons leave the
electroscope it leaves the electroscope with a net positive charge. When you withdraw
the rod, the electroscope will remain with a net positive charge, since you drained it of
electrons.
Example of Induction With an Electroscope
By touching the metal sphere you are grounding the electroscope, instead of the finger
you can use the GND symbol shown in Figure 1.
Coulomb’s Law of Electrostatic Attraction
You will be verifying Coulomb’s law, with some very high tech equipment. Two
balloons, a piece of fur, a meter ruler and some string hanging from the ceiling! You
should be familiar with Coulomb’s law from lecture… it is basically an inverse square
law between two charges. Like charges repel, unlike charges attract. We will explain
the details in Experiment 2 below.
What You Need To Do:
There are two experiments to perform. The first involves charging up some objects
and trying to determine whether you have a positive or negative charge on the object.
You will accomplish this by using an electroscope. You are given that the gray rod
and fur will leave you with a negatively charged rod and the fur will be positively
charged. The second experiment involved Coulombs law verification using charged
balloons.
1-2
Electrostatics and Coulomb’s Law
Physics 226 Lab
Experiment 1
Part 1 – Electroscope Use the gray rod to charge the electroscope by conduction …
charge the gray rod and slide it across the metal sphere on top of the electroscope, you
may need to do this several times, charging the rod between each go, to get a good
charge on the electroscope. The gold leaves should remain far apart. Note that
electrons are transferred to the electroscope during this process leaving it negatively
charged (excess of electrons). If you bring a negatively charged rod close (but not
touching) the metal sphere, the gold leaves will separate further. If you bring a
positively charged rod close to the metal sphere the leaves will fall, since electrons
are being attracted to the sphere to be close to the positive rod. Fill in the table below,
say if your rod is charged positive or negative, a lot or a little.
Metal Sphere
Fur
Red Cloth
Plastic Bag
Polypropylene (White)
Glass
PVC (Gray)
Acrylic (Clear)
Nylon (Beige)
Question 1 Why should the weather affect your results? Think about humidity and
conduction of charge through the air.
If you need to discharge your electroscope, simply ground it by touching the top.
You can ground the rods in the same way, just handle them for a little while and they
discharge through you to ground.
Part 2 – Faraday’s Cup Remove the metal sphere from the top of the electroscope.
Repeat Part 1 above, pay particular attention to those entries where you said the
charge was small or no charge at all. Why do you think the cup makes the charge
increase? Look it up online to find out!
Faraday’s Cup
Fur
Polypropylene (White)
Glass
PVC (Gray)
Acrylic (Clear)
Nylon (Beige)
1-3
Red Cloth
Plastic Bag
Electrostatics and Coulomb’s Law
Physics 226 Lab
Experiment 2: Coulomb’s Law
You are given that the gray rod and fur will leave you with a negatively charged rod
and the fur will be positively charged. The second experiment involved Coulombs
law verification using charged balloons.
Charge up your electroscope using the gray PVC rod. This will give a negatively
charged scope.
Weigh the balloons, using the scale at the front of the class, there are spare ballons
there if you need to wait.
Blow up your 2 balloons tie a knot and charge them by rubbing with fur. Try to get an
even charge by rubbing all over the balloon not just one part, the rubber of the balloon
is an insulator so charge tends to stay in one place.
Using your electroscope discover whether the balloon is positively or negatively
charged.
The Balloon mass is __________kg (1000g = 1 kg)
Balloon charge is _______(+/-).
• Now tie the balloons to the 2 strings hanging down from the ceiling. They will
most likely discharge during this process so once they’re hung, charge them again.
The balloons should separate from each other and make a 10 or 20 degree angle at
the ceiling.
• Measure the length of the string from the ceiling to the middle of the balloon.
• Measure the angle by measuring the mid-point to mid-point separation of the
balloons. You should be able to get this to about 1 or 2 cm accuracy, that’s good
enough. Use half this separation and the length of the string to determine the angle.
L = _________ m, d = _________m, θ = _________degrees. [Where tan θ = d/(2L)]
OK now for the real physics. We’ll start with a free body diagram for one balloon.
We’ll treat the balloon as a point (which you can think of as the center of the balloon).
1-4
Electrostatics and Coulomb’s Law
Physics 226 Lab
Below is a Free Body Diagram (FBD) of the forces on the balloon. There is tension
weight and Coulomb repulsion. These forces must balance for the balloon to be
stationary.
Constants
ε o = 8 . 85 x 10 −12
C2
N ⋅m2
g = 9 .81 m / s 2
Now consider balancing horizontal and vertical forces.
Horizontally we have: T sin θ = F
(1)
Vertically we have:
(2)
T cos θ = mg
If we divide (1) by (2) we get; tan θ =
F
d
=
mg 2 L
q2
(3)
Coulomb’s force law says;
F=
This implies that,
d3 =
Lq 2
2 πεo mg
(5)
Hence;
q =
2 πε o mgd 3
L
(6)
4 πε o d 2
(4)
Show work below to derive equation (6) using equations (3) and (4).
1-5
Electrostatics and Coulomb’s Law
Physics 226 Lab
Find q then divide by the electronic charge e to find the number of electrons either
extra on the balloon or missing from the balloon (depending on whether it is +/- ).
The charge is likely very small like … 20 x 10-9 C to 200 x 10-9 C … something of
that order. Depends on the weather a bit, humidity.. you want a dry day.
No. of charges N = _____________.
something … x 1011 or x 1012)
(This should be a VERY large number
To complete this lab please answer the following questions:
1. Which force was NOT on the free body diagram?
a. Tension
b. Weight
c. Coulomb force
d. Normal force
2. We rub completely around the balloons to give them charge. Could achieve an equal
charge distribution by just rubbing one side of the balloon?
a. Yes, because the charge will spread out equally around the balloon
b. No, because the balloon is an insulator and the charge will stay local.
c. Yes, because the charge can move through the air inside the balloon to the other
side.
d. No, because the protons removed from the balloon to the fur do not shift.
3. You measured the radius between the balloons 3 times and found values of
13.0
cm, 13.5 cm, and 15.0 cm. The correct way to present the average value with error
would be;
a. 13.8 ± 2.0 cm
b. 13.8 ± 1.0 cm
c. 14.0 ± 1.0 cm
d. 14.0 ± 2.0 cm
e. 13.5 ± 1.0 cm
4. The picture on the left shows a situation where balloon B has twice the angle of
balloon This could occur if;
a. Balloon A weighs more than balloon B, both same charge.
b. Balloon B weighs more than balloon A, both same charge.
c. Balloon B has more charge than balloon A both weigh the same.
d. More than one answer above is correct.
e. This cannot happen ;-) oh yes it can!
5. Two small charged objects attract each other with a force F when separated by a
distance d. If the charge on each object is reduced to one-fourth of its original value
and the distance between them is reduced to d/2 the force becomes:
a. F/16
b. F/8
c. F/4
d. F/2
e. F
1-6
Electrostatics and Coulomb’s Law
6. The units of
1
4 πε o
Physics 226 Lab
are:
a. N 2 C 2
N ⋅m
b.
C
c.
d.
e.
N2 ⋅m2
C2
N ⋅m2
C2
m2
C2
7. The leaves of a positively charged electroscope diverge more when an object is brought
near the knob of the electroscope. The object must be:
a. a conductor
b. an insulator
c. positively charged
d. negatively charged
e. uncharged
8. Two particles, each with charge Q, and a third
particle, with charge q, are placed at the
vertices of an equilateral triangle as shown.
The force on the particle with charge q is:
a. Parallel to the left side of the triangle
b. Parallel to the right side of the triangle
c. Parallel to the bottom side of the triangle
d. Perpendicular to the bottom side of the
triangle
e. Perpendicular to the left side of the triangle
Previous Results:
Balloon mass 2 g = 2 x 10-3 kg, length of string
L = 210 cm = 2.1 m, separation d = 20 cm = 0.2 m,
θ = 5.4º.
Using constants provided …
we found q = 182.4 nC
and hence # electrons = N = 1.14 x1012 electrons
Good luck… try not to let the balloons touch you
or furniture once they’re charged. Have fun!!
1-7