Physics 121: Electricity &
Magnetism – Lecture 2
Electric Charge
Dale E. Gary
Wenda Cao
NJIT Physics Department
Electricity in Nature
Most dramatic natural
electrical phenomenon is
lightning.
 Static electricity (balloons,
comb & paper, shock from
a door knob)
 Uses—photocopying, ink-jet
printing

September 5, 2007
Static Charge
1. How can I demonstrate static charge using an
inflated balloon?
A.
B.
C.
D.
E.
Pop it. The sound it makes is due to static charge.
Rub it on cloth, rug, or hair, then it will stick to a wall.
Rub it on a metal surface, then use it to pick up bits of
paper.
Drop it and time its fall. If it falls slower than a rock, it
is affected by static charge.
Let the air out slowly. It will be larger than its original
size due to static charge.
September 5, 2007
Demonstrations of Electrostatics
 Balloon
 Glass
rod/silk
 Plastic rod/fur
 Electroscope
 Van de Graaf Generator
September 5, 2007
Glass Rod/Plastic Rod







A glass rod rubbed with silk gets a positive charge.
A plastic rod rubbed with fur gets a negative
charge.
Suspend a charged glass rod from a thread, and
another charged glass rod repels it.
A charged plastic rod, however, attracts it.
This mysterious force is called the electric force.
Many similar experiments of all kinds led Benjamin
Franklin (around 1750) to the conclusion that there
are two types of charge, which he called positive
and negative.
He also discovered that charge was not created by
rubbing, but rather the charge is transferred from
the rubbing material to the rubbed object, or vice
versa.
September 5, 2007
Forces Between Charges
 We
observe that
Like charges repel each other
Opposite charges attract each other
September 5, 2007
Electroscope
This is a device that can visually show
whether it is charged with static
electricity.
 Here is an example charged positive.
 Notice that the charges collect near
the ends, and since like charges repel,
they exert a force sideways.

------
You can make the deflection arm
move by adding either positive or
negative charge.
 BUT, we seem to be able to make it
move without touching it.
 What is happening?

Electrostatic Induction
September 5, 2007
The Atom

We now know that all atoms are made of positive charges in the nucleus,
surrounded by a cloud of tiny electrons.
Electron
Proton
Neutron
Proton charge +e, electron charge -e
where e = 1.60210-19 C
More accurate picture of the
atom—the Helium atom
September 5, 2007
The Atom

We now know that all atoms are made of positive charges in the nucleus,
surrounded by a cloud of tiny electrons.

Atoms are normally neutral,
meaning that they have
exactly the same number of
Electron
protons as they do electrons.
The charges balance, and the
Proton 
atom has no net charge.
Neutron
Proton charge +e, electron charge -e
where e = 1.60210-19 C
2. Which type of charge
is easiest to remove
from an atom?
A.
Proton
B.
Electron
September 5, 2007
The Atom

In fact, protons are VASTLY more difficult to remove, and for all practical
purposes it NEVER happens except in radioactive materials. In this course,
we will ignore this case. Only electrons can be removed.
3. If we remove an
electron, what is the
net charge on the
atom?
A.
Positive
B.
Negative
Proton charge +e, electron charge -e
where e = 1.60210-19 C
If we cannot remove a proton, how do
we ever make something charged
negatively? By adding an “extra”
electron.
September 5, 2007
Glass Rod/Plastic Rod Again
We can now interpret what is happening with the
glass/plastic rod experiments.
 Glass happens to lose electrons easily, and silk
grabs them away from the glass atoms, so after
rubbing the glass becomes positively charged and
the silk becomes negatively charged.
 Plastic has the opposite tendency. It easily grabs
electrons from the fur, so that it becomes positively
charged while the fur becomes negatively charged.

The ability to gain or lose electrons through rubbing
is called Triboelectricity.
Tribo means rubbing
September 5, 2007
Triboelectric Series
Most Positive
(items on this end lose electrons)
Most Negative
(items on this end steal electrons)
asbestos
rabbit fur
glass
hair
nylon
wool
silk
paper
cotton
hard rubber
synthetic rubber
polyester
styrofoam
orlon
saran
polyurethane
polyethylene
polypropylene
polyvinyl chloride (PVC pipe)
teflon
silicone rubber
September 5, 2007
Insulators and Conductors
Both insulators and conductors can be charged.
Insulator
 The difference is that



On an insulator charges are not able to move from
place to place. If you charge an insulator, you are
typically depositing (or removing) charges only from
the surface, and they will stay where you put them.
On a conductor, charges can freely move. If you try
to place charge on a conductor, it will quickly spread
over the entire conductor.
Conductor
September 5, 2007
Insulators and Conductors
4. Which of the following is a good
conductor of electricity?
A
B. A
C. A
D. A
E. A
A.
plastic rod.
glass rod.
rock.
wooden stick.
metal rod.
September 5, 2007
Metals and Conduction
Notice that metals are not only good electrical conductors, but they are also
good heat conductors, tend to be shiny (if polished), and are maleable (can
be bent or shaped).
 These are all properties that come from the ability of electrons to move
easily.
This iron atom (26 protons, 26 electrons) has
two electrons in its outer shell, which can
move from one iron atom to the next in a
metal.

Path of electron
in a metal
September 5, 2007
Van de Graaf Generator

Rubber band steals electrons from
glass

Glass becomes positively charged

Rubber band carries electrons
downward
Positively charged glass continues
to rotate
Wire “brush” steals electrons from
rubber band
Positively charged glass steals
electrons from upper brush




Sphere (or soda can) becomes
positively charged—to 20,000 volts!
September 5, 2007
Electric Force and Coulomb’s Law

We can measure the force of attraction or repulsion between charges, call
them q1 and q2 (we will use the symbol q or Q for charge).
q1
q2
r
 When we do that, we find that the force is proportional to the each of the
charges, is inversely proportional to the distance between them, and is
directed along the line between them (along r).
q1
q2
q q
In symbols, the magnitude of the force is F  k 1 2 2
where k is some
r
constant of proportionality.
 This force law was first studied by Coulomb in 1785, and is called
Coulomb’s Law. The constant k = 8.98755109 N m2/C2 is the Coulomb
constant.

September 5, 2007
Electric Force and Coulomb’s Law
Although we can write down a vector form for the force, it is easier to
simply use the equation for the magnitude, and just use the “like charges
repel, opposites attract” rule to figure out the direction of the force.
 Note that the form for Coulomb’s Law is exactly the same as for
gravitational force between two masses
Note BIG difference,
Gk
m1m2
F G 2
There is only one “sign”
m

q
r

of mass, only attraction.
Note also that the mass is an intrinsic property of matter. Likewise, charge
is also an intrinsic property. We only know it exists, and can learn its
properties, because of the force it exerts. Full form of Coulomb’s Law
 Because it makes other equations easier to write, Coulomb’s constant is
1
actually written
1 q1 q2
k
F
4e0
4e0 r 2

where e0 = 8.8510-12 C2/N-m2 is called the permittivity constant.
September 5, 2007
Spherical Conductors
Because it is conducting, charge on a metal sphere will go everywhere over
the surface.
 You can easily see why, because each of the charges pushes on the others
so that they all move apart as far as they can go. Because of the symmetry
of the situation, they spread themselves out uniformly.
 There is a theorem that applies to this case, called the shell theorem, that
states that the sphere will act as if all of the charge were concentrated at
the center.

Note, forces are equal and opposite
These two situations are the same
September 5, 2007
Insulators and Conductors
5. Two small spheres are charged with equal and opposite
charges, and are placed 30 cm apart. Then the charge
on sphere 1 is doubled. Which diagram could be
considered to show the correct forces?
2q
-q
A.
B.
C.
D.
E.
September 5, 2007
Case of Multiple Charges

You can determine the force on a particular charge by adding up all of the
forces from each charge.
Forces on one charge due to a number
of other charges
September 5, 2007
Charges in a Line
6. Where do I have to place the + charge in order for
the force to balance, in the figure at right?
A.
Cannot tell, because + charge value is not
given.
B.
Exactly in the middle between the two negative
charges.
C.
On the line between the two negative charges,
but closer to the -2q charge.
D.
On the line between the two negative charges,
but closer to the -q charge.
E.
There is no location that will give force balance.
-2q
-q
September 5, 2007
Let’s Calculate the Exact Location
Force is attractive toward both negative charges, hence could
balance.
 Need a coordinate system, so choose total distance as L, and
position of + charge from -q charge as x.
 Force is sum of the two force vectors, and has to be zero, so
2qQ
qQ
F  F1 + F2  k
k
0
2
2
( L - x)
x
 A lot of things cancel, including Q, so our answer does not
depend on knowing the + charge value. We end up with

2
1

( L - x) 2 x 2

( L - x) 2
L-x

2

 2
x2
x
-2q
L
x
L
 0.412 L , so slightly less than halfSolving for x, x 
1+ 2
way between.
September 5, 2007
-q
Summary







Charge is an intrinsic property of matter.
Charge comes in two opposite senses, positive and negative.
Mobil charges we will usually deal with are electrons, which can be removed
from an atom to make positive charge, or added to an atom to make
negative charge. A positively charged atom or molecule can also be mobil.
There is a smallest unit of charge, e, which is e = 1.60210-19 C. Charge
can only come in units of e, so charge is quantized. The unit of charge is
the Coulomb.
Charge is conserved. Charge can be destroyed only in pairs (+e and –e can
annihilate each other). Otherwise, it can only be moved from place to
place.
Like charges repel, opposite charges attract.
1 q1 q2
F

The electric force is give by Coulomb’s Law:
4e0 r 2
Materials can be either conductors or insulators.
Conductors and insulators can both be charged by adding charge, but
charge can also be induced.
 Spherical conductors act as if all of the charge on their surface were
concentrated at their centers.


September 5, 2007