Electrostatics

1
Electrostatics

• Electric charge
• Conservation of charge
• Insulators conductors
• Charging objects
• Electroscopes
• Lightning

• Van de Graff generators
• Equilibrium problems
• Grounding
• Static electricity
• Coulombs law
• Systems of charges

2
Electric Charge

• Just as most particles have an attribute known
  as mass, many possess another attribute called
  charge. Charge and mass are intrinsic properties,
  defining properties that particles possess by
  their very nature.
• Unlike mass, there are two different kinds of
  charge positive and negative.
• Particles with a unlike charges attract, while
  those with like charges repel.
• Most everyday objects are comprised of billions
  of charged, but usually there are about the same
  number of positive charges as negative, leaving
  the object as a whole neutral.
• A charged object is an object that has an excess
  of one type of charge, e.g., more positive than
  negative. The amount of excess charge is the
  charge we assign to that object.

3
Conservation of Charge
Charged particles can be transferred from one
object to another, but the total amount of charge
is conserved. Experiments have shown that
whenever subatomic particles are transferred
between objects or interact to produce other
subatomic particles, the total charge before and
after is the same (along with the total energy
and momentum). Example An object with 5 excess
units of positive charge and another with 2 units
of excess negative charge are released from rest
and attract each other. (By Newtons 3rd law, the
forces are equal strength, opposite directions,
but their accelerations depend on their masses
too.) Since there is no net force on the system,
their center of mass does not accelerate, and
they collide there. As they fall toward each
other, electric potential energy is converted to
kinetic energy. When contact is made charge may
be exchanged but they total amount before and
after must be the same. After the collision the
total momentum must still be zero.
Before
After
1.5
1.5
5
-2
Total charge 3
Total charge 3
4
Conservation of Charge ß-decay

• The stability of the nucleus of an atom depends
  on its size and its proton-neutron ratio. This
  instability sometimes results in a radioactive
  process known as ß-decay.
• A neutron can turn into a proton, but in the
  process an electron (beta particle) is ejected at
  high speed from the nucleus to conserve charge.
• A proton can turn into a neutron. In this case
  the beta particle is an positron (an
  antielectron same mass as an electron but a
  positive charge) to make up for the loss of
  positive charge of the proton.
• In either case, charge, momentum, and energy are
  conserved.

5
SI unit of Charge the Coulomb

• Just as we have an SI unit for mass, the
  kilogram, we have one for charge as well. Its
  called the coulomb, and its symbol is C.
• Its named after a French physicist, Charles
  Coulomb, who did research on charges in the mid
  and late 1700s.
• A coulomb is a fairly large amount of charge, so
  sometimes we measure small amounts of charge in
  µC (mircocoloumbs).
• An electron has a charge of -1.6 ? 10-19 C.
• A proton has a charge of 1.6 ? 10-19 C.
• In a wire, if one coulomb of charge flows past a
  point in one second, we say the current in the
  wire is one ampere.

6
Elementary Charge

• Charges come in small, discrete bundles. Another
  way to say this is that charge is quantized. This
  means an object can possess charge in
  incremental, rather than continuous, amounts.
• Imagine the graph of a linear function buy when
  you zoom in very close you see that it really is
  a step function with very small steps.
• The smallest amount of charge that can be added
  or removed from an object is the elementary
  charge, e 1.6 ? 10-19 C.
• The charge of a proton is e, an electron -e.
• The charge of an object, Q, is always a multiple
  of this elementary charge Q N e, where N is
  an integer.
• How many excess protons are required for an
  object to have 1 C of charge?

7
Insulators vs. Conductors

• A conductor is a material in which excess charge
  freely flows. Metals are typically excellent
  conductors because the valence (outer shell)
  electrons in metal atoms are not confined to any
  one atom. Rather, they roam freely about a metal
  object. Metal are excellent conductors of
  electricity (and heat) for this reason.
• An insulator is a material in which excess
  charge, for the most part, resides where it is
  deposited. That is, once placed, it does not
  move. Most nonmetallic material are good
  insulators. Valence electrons are much more
  tightly bound to the atoms and are not free to
  roam about. Insulators are useful for studying
  electrostatics (the study of charge that can be
  localized and contained).
• Semi-conductors, like silicon used in computer
  chips, have electrical conductivity between that
  of conductors and insulators.

Details on Conductors, Semiconductors, and
Insulators
8
Electrons and Chemical Bonds
All chemical bonding is due to forces between
electrostatic charges. Covalent bonding A pair
of electrons is shared between two nonmetal
atoms, allowing each atom to have access to
enough electrons to fill its outer shell. Except
for hydrogen, this usually means 8 electrons in
the outer shell (octet rule). Ionic bonding One
or more valence electrons of a metal atom are
stolen by a nonmetal atom, leaving a positive
metal ion and a negative nonmetal ion, which then
attract one another. Metallic bonding Valence
electrons of metals flow freely throughout a
metal object. These delocalized electrons are
attracted to the nuclei of the atoms through
which they are moving about. This produces a
strong binding force that holds the atoms
together. In an iron bar, for example, there is
no covalent or ionic bonding. Metallic bonding
hold the metal together.
9
Charging up Objects

• Charging up an object does not mean creating new
  charges. Charging implies either adding electrons
  to an object, removing electrons from an object,
  or separating out positive and negative charges
  within an object. This can be accomplish in 3
  different ways
• Friction Rubbing two materials together can rub
  electrons off of one and onto the other.
• Conduction Touching an object to a charged
  object could lead to a flow of charge between
  them.
• Induction If a charged object is brought near
  (but not touching) a second object, the charged
  object could attract or repel electrons
  (depending on its charge) in the second object.
  This yields a separation charge in the second
  object, an induced charge separation.

10
Electroscopes
Electroscopes
An electroscope is an apparatus comprised of a
metal sphere and very light metal leaves. A metal
rod connects the leaves to the sphere. The leaves
are enclosed in an insulating, transparent
container. When the electroscope is uncharged the
leaves hang vertically. The scope is charged by
placing a charged rod near the sphere. The rod is
charged by friction. If a rubber rod is rubbed
with fur, electrons will
be rubbed off the fur and
onto the rubber rod, leaving the rod negatively
charged. If a glass rod is rubbed with silk,
electrons will be rubbed off the rod onto the
silk, leaving the glass rod positively charged.
Either rod, if brought near, will charge the
scope by induction. Also, either rod, if contact
is made with the sphere, will charge the scope by
conduction.
continued
11
Electroscopes (cont.)
When a positively charged rod is placed near but
not touching the metal sphere, some of the
valence electrons in the metal leaves are drawn
up into the sphere, leaving the sphere negatively
charged and the leaves positively charged. Thus,
the rod has induced a charge
separation in the scope. The light, positive
leaves repel each other and separate. The
electroscope as a whole is still electrically
neutral, but it has undergone a charge
separation. As soon as the rod is removed from
the vicinity, the charge separation will cease to
exist and the leaves the drop. Note Only the
electron are mobile the positives on the leaves
represent missing electrons.

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continued
12
Electroscopes (cont.)
When a negatively charged rod is placed near but
not touching the metal sphere, some of the
valence electrons in the sphere are repelled down
into the metal leaves, leaving the sphere
positively charged and the leaves negatively
charged. The rod has again induced a charge
separation in the scope. The light, negative
leaves repel each other as before. Again, the
electroscope as a whole is electrically neutral,
but the charge separation will remain so long as
the rod remains nearby. Note that this situation
is indistinguishable from the situation with the
positive rod. Since the effects are the same, how
do we know that the rods really do have different
charges?
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continued
13
Electroscopes (cont.)
Now lets touch the negative rod to the sphere.
Some of the electrons can actually hop onto the
sphere and spread throughout the scope. This is
charging by conduction since, instead of
rearranging charges in the scope, new charges
have been added the scope is no longer neutral.
The extra electrons force the leaves apart, even
when the rod is removed. If the negative rod
returns, it charges the leaves further, but this
time by induction (by driving some of
- - - - - - - - - - - - - - - - - - - - -
electrons on the sphere down to the leaves). This
causes an increased separation of the leaves.
When the rod is removed, the scope will return to
the state on the left.
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Continued
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extra e- s added
leaf spread increases
14
Electroscopes (cont.)
The pic on the left shows a scope that has
acquired extra electrons from a negative rod that
has since been removed. Now we bring a positive
rod nearby. This has the opposite effect of
bringing the negative rod near. This time some of
the extra electrons in the leaves head to the
sphere and the spread of the leaves diminishes.
Note the scope is still negatively charged
overall, but the presence of the
positive rod means more of the excess negative
charge will reside in the sphere and less in the
leaves. When the rod is removed, the scope return
to the state on the left.

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Continued
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extra e- s added
leaf spread decreases
15
Grounding an Electroscope
Whether a scope has charged by conduction, either
positively or negatively, the quickest way to
uncharge it is by grounding it. To do this we
simply touch the sphere. When a negatively
charged scope is grounded by your hand, the
excess electrons from the scope travel into your
body and, from there, into your surroundings.
When a
positively charged scope is grounded, electrons
from your body flow into the scope until it is
neutral. Your surroundings will replace the
electrons youve donated to the scope. As always,
its only the electrons that move around.
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16
Electroscope Practice Problem
For the following scenario, try to predict what
would happen after each step. Explain each in
terms of electrons and charging.

1. A rod is rubbed with a material that has a
   greater affinity for electrons than the rod
   does.
2. This rod is brought near a neutral electroscope.
   
3. This rod touches the electroscope and is
   removed.
4. A positive rod is alternately brought near and
   removed.
5. A negative rod is alternately brought near and
   removed.
6. Finally, you touch the scope with your finger.

17
Redistributing Charge on Conducting Spheres
Two neutral spheres, A B, are placed side by
side, touching. A negatively charged rod is
brought near A, which induces a charge separation
in the A-B system. Some of the valence e-s in
A migrate to B. When the rod is re-moved and A
B are separated, A is , B is -, but the system
is still neutral.
-Q
Q
- - - - - - - -
B
A
A is now brought near neutral sphere C, inducing
a charge separation on it. Valence e-s in C
migrate toward A, but since C is being touched on
the positive side, e-s from the hand will move
into C. Interestingly, C retains a net negative
charge after A and the hand are removed even
though no charged object ever made contact with
it.
Q
-
A
C
18
Static Electricity Shocks
If you walk around on carpeting in your stocking
feet, especially in the winter when the air is
dry, and then touch something metal, you may feel
a shock. As you walk you can become negatively
charged by friction. When you make contact with a
metal door knob, you discharge rapidly into the
metal and feel a shock at the point of contact. A
similar effect occurs in the winter when you exit
a car if you slide out of your seat and touch
then touch the car door, you might feel a
shock. The reason the effect most often occurs in
winter is because the air is typically drier
then. Humidity in the air can rather quickly rob
excess charges from a charged body, thereby
neutralizing it before a rapid, localized
discharge (and resulting shock) can take place.
Care must be taken to prevent static discharges
where sensitive electronics are in use or where
volatile substances are stored.
19
Static Electricity Balloons
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1
Pic 1 If you rub a balloon on your hair,
electrons will be rubbed off your hair onto the
balloon (charging by friction). Pic 2 If you
then place the negatively charged balloon near a
neutral wall, the balloon will repel some of the
electrons near it in the wall. This is inducing a
charge separation in the wall. Now the wall,
while still neutral, has a positive charge near
the balloon. Thus, the balloon sticks to the
wall. Pick 3 Your hair now might stand up.
This is because it has been left positively
charged. As with the leaves of a charged
electroscope, the light hairs repel each other.
2
3
20
Hanging Balloons
1
You hang two balloons from the ceiling and rub
them on your hair.
2
When you move out of the way, the negatively
charged balloons repel each other. On each
balloon there are three forces tension in the
string, gravity, and the electric force. The
angle of separation will grow until equilibrium
is achieved (zero net force).
3
If you move your head close to either of the
balloons, it will move toward you since your hair
remains positively charged.
21
Polarization of a Cloud
Lightning is the discharge of static electricity
on a massive scale. Before a strike the bottom
part of a cloud becomes negatively charged and
the top part positively charged. The exact
mechanism by which this polarization (charge
separation) takes place is uncertain, but this is
the precursor to a lightning strike from cloud to
cloud or cloud to ground.
One mechanism incorporates friction when moist,
warm air rises, it cools and water droplets form.
These droplets collide with ice crystals and
water droplets in a cloud. Electrons are torn off
the rising water droplets by the ice crystals.
The positive droplets rise to the top of the
cloud, while the negative ice crystals remain at
the bottom. A second mechanism involves the
freezing process experiments have shown that
when water vapor freezes the central ice crystal
becomes negatively charged, while the water
surrounding it becomes positive. If rising air
tears the surrounding water from the ice, the
cloud becomes polarized. There are other
theories as well.
Detailed Lightning Diagrams
22
Lightning Strikes
The negative bottom part of the cloud induces a
charge separation in the ground below. Air is
normally a very good insulator, but if the charge
separation is big enough, the air between the
cloud and ground can become ionized (a plasma).
This allows some of the electrons in the cloud to
begin to migrate into the ionized air below. This
is called a leader. Positive ions from the
ground migrate up to meet the leader. This is
called a streamer. As soon as the leader and
streamer meet, a fully conductive path exists
between the cloud and ground and a lightning
strike occurs. Billions of trillions of electrons
flow into the ground in less than a millisecond.
The strike can be hotter than the surface of the
sun. The heat expands the surrounding air which
then claps as thunder.









23
Lightning Rods and Grounding
Discovered by Ben Franklin, a lightning rod is a
long, pointed, metal pole attached to a building.
It may seem crazy to attract lightning close to a
susceptible structure, but a lightning rod can
afford some protection. When positive charges
accumulate beneath a cloud, the accumulation is
extremely high near the tip of the rod. As a
result, an electric field is produced that is
much greater surrounding the tip than around the
building. (Well study electric fields in the
next unit.) This strong electric field ionizes
the air around the tip of the rod and
encourages a strike to occur there. If a
strike does occur, the electricity travels down
the rod into a copper cable that connects the
lightning rod to a grounding rod buried in the
earth. There the excess charge is grounded, i.e.,
the electrons are dissipated throughout the
landscape. By taking this route, rather than
through a building and its wiring, much loss is
prevented.
24
Van de Graaff Generator
A Van de Graaff generator consists of a large
metal dome attached to a tube, within which a
long rubber belt is turning on rollers. As the
belt turns friction between it and the bottom
roller cause the e-s to move from the belt to
the roller. A metal brush then drains these e-s
away and grounds them. So, as the belt passes the
bottom roller it acquires a positive charge,
which is transported to the top of the device
(inside the dome). Here another metal brush
facilitates the transfer of electrons from the
dome to the belt, leaving the dome positively
charged. In short, the belt transports electrons
from a metal dome to the ground, producing a very
positively charged dome. No outside source of
charge is required, and the generator could even
be powered by a hand crank. A person touching the
dome will have some of her e-s drained out. So,
her lightweight, positive hair will repel itself.
Coming close to the charge dome will produce
sparks when electrons jump from a person to the
dome.
Internal workings
Detailed explanation
25
Coulombs Law
There is an inverse square formula, called
Coulombs law, for finding the force on one point
charge due to another
K 9 ? 109 N m2 / C2
This formula is just like Newtons law of uniform
gravitation with charges replacing masses and K
replacing G. It states that the electric force
on each of the point charges is directly
proportional to each charge and inversely
proportional to the square of the distance
between them. The easiest way to use the formula
to ignore signs when entering charges, since we
already know that like charges repel and
opposites attract. K is the constant of
proportionality. Its units serve to reduce all
units on the right to nothing but newtons. Forces
are equal but opposite.
r
F
F

-
q1
q2
Coulomb's Law Detailed Example
Charges in Motion
26
Electric Force vs. Gravitational Force
K q1 q2
K 9 ? 109 N m2 / C2
FE
r 2
G m1 m2
G 6.67 ? 10-11 N m2 / kg2
FG
r 2
Gravity is the dominant force when it comes to
shaping galaxies and the like, but notice that K
is about 20 orders of magnitude greater than G.
Technically, they cant be directly compared,
since they have different units. The point is,
though, that a whole lot of mass is required to
produce a significant force, but a relatively
small amount of charge can overcome this,
explaining how the electric force on a balloon
can easily match the balloons weight. When
dealing with high-charge, low-mass objects, such
as protons electrons, the force of gravity is
negligible.
27
Electric Force Example
A proton and an electron are separated by 15 µm.
They are released from rest. Our goal is to find
the acceleration each undergoes at the instant of
release.

1. Find the electric force on each particle.
2. Find the gravitational force on each particle. A
   protons mass is 1.67 ? 10-27 kg, and an
   electrons mass is 9.11 ? 10-31 kg.
3. Find the net force on each and round
   appropriately. Note that the gravitational force
   is inconsequential here.
4. Find the acceleration on each particle.
5. Why couldnt we use kinematics to find the time
   it would take the particles to collide?

1.024 10-18 N
4.51 10-58 N
1.024 10-18 N
e- 1.124 1012 m/s2, p 6.13 108 m/s2
r changes, so F changes, so a changes.
15 µm


28
System of 3 Charges
In a system of three point charges, each charge
exerts a forces on the other two. So, here weve
got a vector net force problem. Find the net
force on charge B. Steps

1. Find the distance in meters between A and B
   using the law of cosines.
2. Find angle B in the triangle using the law of
   sines.
3. Find FBA (the magnitude of the force on charge
   B due to charge A).
4. Find FBC.
5. Break up the forces on B into components and
   find the net horiz. vertical forces.
6. Determine Fnet on B.

0.261947 m
A
3 µC
36.027932 º
0.786981 N
17 cm
4.591836 N
115º
C
3.78 N (right) , 1.25 N (up)
B
-5 µC
14 cm
3.98 N at 18.3 º N of E
2 µC
29
System of 4 Charges
Here four fixed charges are arranged in a
rectangle. Find Fnet on charge D. Solution
-16 µC
25 µC
A
C
767.2 N at 59.6 º N of W
4 cm
B
D
9 µC
-7 µC
3 cm
Link
30
Hanging Charge Problem
Two objects of equal charge and mass are hung
from the same point on a ceiling with equally
long strings. They repel each other forming an
angle ? between the strings. Find q as a
function of m, L and ?. Solution Draw a
f.b.d. on one of the objects, break T into
components, and write net vertical and horiz.
equations T sin(? / 2) FE , T cos(? / 2)
mg. Dividing equations and using Coulombs law
yields mg tan(? / 2) FE Kq 2 / r 2, where
r 2 L sin(? / 2). Thus,
?
L
L
T
q, m
q, m
FE
mg
4 L2 mg tan(? / 2) sin2(? / 2)
q
K
31
Point of Equilibrium
Clearly, half way between two equal charges is a
point of equilibrium, P, as shown on the left.
(This means there is zero net force on any charge
placed at P.) At no other point in space, even
points equidistant between the two charges, will
equilibrium occur. Depicted on the right are two
positive point charges, one with twice the charge
of the other, separated by a distance d. In
this case, P must be closer to q than 2 q
since in order for their forces to be the same,
we must be closer to the smaller charge. Since
Coulombs formula is nonlinear, we cant assume
that P is twice as close to the smaller charge.
Well call this distance x and calculate it in
terms of d.
Continued
x ?
P
P
q
q
q
2 q
d
32
Point of Equilibrium (cont.)
Since P is the equilibrium point, no matter what
charge is placed at P, there should be zero
electric on it. Thus an arbitrary test charge
q0 (any size any sign) at P will feel a force due
to q and an equal force due to 2 q. We
compute each of these forces via Coulombs law
The Ks, qs, and q0s cancel, the latter
showing that the location of P is independent of
the charge placed there. Cross multiplying we
obtain
K q q0
K (2 q) q0

x 2
(d - x)2
(d - x)2 2 x 2 ? d 2 - 2 x d x 2 2 x 2
? x 2 2 x d - d 2 0.
33
Point of Equilibrium (cont.)
From x 2 2 x d - d 2 0, the quadratic
formula yields
-2 d ? (2 d )2 - 4 (1) (-d 2 )
-2 d ? 8 d 2
x

2 (1)
2
-d ? d 2 Since x is a distance, we
choose the positive root
x d ( 2 - 1 ) ? 0.41 d. Note that x lt 0.5
d, as predicted.
Note that if the two charges had been the same,
we would have started with (d - x)2 x 2 ?
d 2 - 2 x d x 2 x 2 ? d 2 - 2 x d 0 ?
d (d - 2 x ) 0 ? x d / 2, as predicted.
This serves as a check on our reasoning.
34
Equilibrium with Several Charges
Several equal point charges are to be arranged in
a plane so that another point charge with
non-negligible mass can be suspended above the
plane. How might this be done? Answer Arrange
the charges in a circle, spaced evenly, and fix
them in place. Place another charge of the same
sign above the center of the circle. If placed at
the right distance above the plane, the charge
could hover. This arrangement works because of
symmetry. The electric force vectors on the
hovering charge are shown. Each vector is the
same magnitude and they lie in a cone. Each
vector has a vertical component and a component
in the plane. The planar components cancel out,
but the vertical components add to negate the
weight vector. Continued
35
Equilibrium with Several Charges (cont.)
Note that the charges in the plane are fixed.
That is, they are attached somehow in the plane.
They could, for example, be attached to an
insulating ring, which is then set on a table.
Regardless, how could the arrangement of charges
in the plane be modified so as to maintain
equilibrium of the hovering charge but allow it
to hover at a different height? Answer If the
charges in the plane are arranged in a circle
with a large radius, the electric force vectors
would be more horizontal, thereby working
together less and canceling each other more. The
hovering charge would lower. Since its weight
doesnt change, it must be closer to the plane in
order to increase the forces to compensate for
their partial cancellation. If the charges in the
plane were arranged in a small circle, the
vectors would be more vertical, thereby working
together more and canceling each other less. The
hovering charge would rise and the vectors would
decrease in magnitude. To maximize the height of
the hovering charge, all the charges in the plane
should be brought to a single point. Continued
36
Credits

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emotor/belt.html 207.10.97.102/chemzone/lessons/03
bonding/mleebonding.htm chem.ch.huji.ac.il/eugeni
ik/instruments/archaic/electroscopes.html www.phys
icsclassroom.com/mmedia/estatics/gep.html www.cute
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