Organizational:
New subject: electromagnetism. Same organization as last semester:
1.
Conference on Fridays 8-8:50. Connie Fliegel assigns you. Assingment posted on pinboard soon.
2.
homework due on Tuesdays outside lecture hall. First homework will be assigned tomorrow
3.
three midterm exams. The 2 best count. No makeups. Final exam is May 9 9-12 am
4.
Office hours Monday 10-1 pm. Come at other times too or make appointments.
5.
Grade is 20% conference, 40% midterm exam, 40% final exam.
6.
Please let me hear if you have suggestions for improvements.
A new Fundamental force:
Gravity holds a bowling ball on earth but what holds it together? Last year we learned how to describe its motion and behavior subject to gravity. In thermodynamics we learned that gas and matter in general is built from atoms. But what holds these atoms together to form a bowling ball? It can't be force of gravity because then the ball would not hold together as I lift it away from the earth.
The answer is Electrostatic forces. The electrostatic force is a force between objects that carry net charge. The unit for charge is the Coulomb. (definition later)
We do not experience the electrostatic force on the macroscopic scale because there are two types of charge: positive and negative. If there is equal amounts of each then the total charge is zero and the electrostatic force cancels. Examples of objects with little net charge: The bowling ball, the earth, the sun. That is why we only need to consider the force of gravity between these objects.
How to Experience the Electrostatic Force:
If we disturb the balance of charge then we can experience electrostatic force on the macroscopic scale.
Rub a teflon rod with dry wool adds negative charge to the rod. If we do this on two rods we find that they repel each other.
Glass acts differently: Rubb it and we get a positive charge. Don't worry why it is so. Just notice that we can get an attraction as well as a repulsion between objects that are charged. This is proof of two types of charge we call them positive and negative charge.
Van-de Graaff generator is automated version. We run an electrical motor to build charge on the dome. If we place metallic. There is an internal repulsion between the excess
Collin Leslie Broholm Page 1 01/24/00

ucompensated charge on the dome but it is strong an remains intact. If we place loose metal objects on it they fly off due to the electrostatic repulsion.
Coulombs Law
Experiments show that the electrostatic force has the same form as the gravitational force: It grows with the produce of the charges involved and decreases with the inverse squared distance between the objects:
F
=
1
4
πε
0 q
1 q
2 r
2 q
1
, q
2
are the charges in coulomb of the point objects and r is the distance between them.
Charge is measured in Coulomb (the amount of charge passing through a wire carrying 1
Ampere in 1 sec. ). r is measure in meter (MKS system as always).
ε
0
=
8 .
85
⋅
10
−
12
( )
2
N
−
1
is the vacuum permeability.
Like charges repel each other, different charges attract each other. The sign of charge is a convenient way to build this into the equations:
The two vectors on a given pair are a action reaction pair as described in Newtoms third law.
Just as for gravity Coulombs law obeys the superposition principle . A charged object, q , is subject to the sum of forces from all charged objects surrounding it:
F tot
= ∑ i
F i
= q
4
πε
0
∑ i q r i
2 i r ˆ i
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Applications of Coulombs law:
Quantitative application involving gravity and electrostatic forces
Two very small conducting spheres are suspended from the same point from different strings. The balls are charged and repel each other so both strings form the same angle of
θ
=10 degrees with the vertical direction. What can we say about the mass and charges on the spheres.
In static equilibrium all components of forces vanish. Resolving in the horizontal and vertical directions for the first sphere gives: m
1 g
=
T
1 cos
θ
1
4
πε
0
(
2 l q
1 q sin
2
θ )
2
=
T
1 sin
θ
We are not interested in the tension in the string so we divide it out to give us
4
πε
0 q
1 q
2 l
2
( )
2 m
1 g
= tan
θ sin
2 θ
We see that the product of the charges and the mass enters in determining
θ
. We conclude that if
θ
is the same for the two spheres then their masses must be the same irrespective of how charge is distributed. Measuring the angle determines the product of the charge divided by the mass of the sphere. If we know the mass we can determine the geometric mean of the charge on the conducting spheres: q
=
2 l sin
θ
4
πε
0 mg tan
θ
We can put in numbers using l =1 m, m =0.2 g,
θ
=10 o
to get: q
=
2 m sin 10 4
π
8 .
85
⋅
10
−
12
( )
2
N
−
1
0 .
2
⋅
10
−
3 kg 9.8
m s
2 tan 10
=
6 .
8
⋅
10
−
8
C
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Application where geometrical considerations simplify calculation
Calculate the direction and magnitude of the force on a particle with charge Q in the center of the hexagon shown.
Q Q
Q 2Q
Q Q
We see that most of the forces cancel except for that associated with the excess charge on the 2 Q corner. The net force on the central charge is therefore
F net
=
1
4
πε
0
QQ
!
i r
2
This illustrates that symmetry considerations should be applied when possible rather than brute force in these problems.
Charge is Quantized and Conserved
Experiments show that charge comes in quanta. The basic unit for charge is e= 1.602
.
10
-19
C
Elementary particles carry charge as follows:
−
19
Proton: q neutron: q
= e
=
=
0 e
=
1 .
602
0 C
⋅
10
−
19
C
Charge is a conserved quantity. We check for charge conservation in nuclear fission processes: n
+ 235
92
U
→ 143
56
Ba
+ 90
36
Kr
+
3 n
+ energy
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The supersecript is total number of nucleons (protons and neutrons). The subscript is the number of protons=number of electrons. We notice that the number of electrons and protons and hence charge is conserved. Also the number of neutrons is conserved.
Even when the number of each type of particles change the total charge is conserved as in this beta decay of the free neutron that has a lifetime of about 15 minutes: n
→ e
− + p
+ ν e
ν is a neutrino that carries no charge and very very little mass. The charge adds to zero on both sides of the equation. No process has been documented in which charge conservation is violated so charge is thought to be a conserved property.
Neutral Matter from Balance of Large Amounts of Charge
Macroscopic bodies are generally neutral. They contain lots of charge in the form of electrons and protons but in equal amounts such that there is little or no net charge.
Do you have charge?
A penny has a mass of 3.11 g and is mainly made from copper. It contains
N
= m
M
N
A
=
3 .
11
6 .
022
63 .
5
⋅
10
23 =
2 .
95
⋅
10
22 copper atoms
Each copper atom has 29 electrons and 29 protons. It is therefore a neutral material.
However the total electronic charge is
NZe
=
2 .
95
⋅
10
22
1 .
602
⋅
10
−
19 =
137 kC
This is a very large amount of charge. If the electrons could be completely separated from the protons and kept at 1 km distance then the attractive force
F
=
1
4
πε
0
Q
2 r
2
=
9
⋅
10
9
N
( )
2
(
137
(
⋅ 3
10
1000 m
)
C
2
2
)
=
1 .
7
⋅
10
14
N
This approximately equals the total weight of all motor vehicles in the whole world. No wonder that electrons and protons are held together in neutral atoms molecules and solids and do not exist isolated in substantial quantities.
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Macroscopic Charge Motion in Condensed Matter
Depending on the chemical and physical properties of matter charge can be localized or it can be able to move around. When charge moves in condensed matter it is usually due to motion of the negatively charged electrons. However there are also liquids and solids that conduct through the motion of atoms or molecules.
Insulators:
Charge cannot move through an insulator. Insulators can break down if force on charge carriers becomes sufficiently large. (At finite temperatures the distinction is not so sharp since there is the possibility of some charge transport though not as readily as in a metal)
Good Insulators
Porcelain
Teflon
Plastic and rubber
SF
6
Worse Insulators
Dry air
Pure water
Human body
Metals and Conductors:
Charge can move freely through the material. Electrons are the charge carriers and they take the form of plane waves that move through matter like light moves through empty space. In electrostatic condition (when motion has stoped) no net force acts on any charge in the interior of the material.
Good conductors
Copper
Aluminum
Iron
Mercury
Not so good Conductors
Salt water
Humid air
Human body
Water
Semiconductor:
A material that can be insulator or metal depending on temperature, chemical purity etc. Materials are Ge, Si, GaAs etc.
Superconductor:
Material in which charge can move without dissipation. Can sustain a persistent macroscopic current that is never degraded as long as the material remains superconducting. Most elemental metals become superconductors at sufficiently low T.
Material
Aluminum
Vanadium
Niobium
YBa
2
Cu
3
O
6.5
Collin Leslie Broholm
Critical Temperature (K)
1.2
5.3
9.3
90
Page 6 01/24/00

Electrical Polarizability of Matter
Even neutral matter can exert a force on and be influenced by charged matter. We see some examples:
•
We rub a balloon and can make it stick to the wall. There is no macroscopic motion of charge but individual molecules are slightly polarized or their polarization aligns.
Thinking of the such motion for single molecule we see that if the baloon is negatively charged then negative charge moves away from the balloon and positive charge moves towards it. The repulsive force is then slightly weaker than the attractive force between the molecule and the atom. Multiply this small force by the large number of molecules and you get a force large enough to hold the balloon tightly against the wall so it cannot slide down.
•
We polarize the electroscope. The electroscope remains neutral however the bottom part of the electrode has net charge which is detected as the foil is pushed away from the center of the electrode.
•
Pulling a coke can with a charged stick. The stick shifts electrons towards the far end of the can creating a small macroscopic polarization of the coke can. Because the positive charge is closer to the negatively charged rod there is an attractive force. This force is always attractive irrespective of the charge of the rod.
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