Electrostatic Forces and Coulomb’s Law
Physics
I. Electric Charge
Electric charge is a fundamental property of matter associated with protons
(+) and electrons (-)
When an object gains electrons it becomes (more) negative
When an object loses electrons it becomes (more) positive
When an object becomes charged it is because it has gained or lost
some electrons. These electrons MUST be transferred whole; you
cannot transfer a fraction of an electron. We say that charge is
quantized.
Q = nq
Note: electron charge = qe = -1.6x 10-19C
Proton charge = qp = +1.6x 10-19C
electron mass = me = 9.11 x 10-31 kg
proton mass = mp = 1.67 x 10-27 kg
One Coulomb (C) is the amount of charge on 6 x1018 electrons or protons – it’s HUGE!
Methods of Charging
Demos
Fur and rod
Van de Graff
Video (balloon on
wall)
Demo – water and
comb
1) Friction – transfer of charge requires direct contact. This is a forced
transfer involving the violent removal/addition of electrons.
2) Conduction- transfer of charge requires direct contact. This is the
natural “flow” of charge between two objects when they touch.
3) Induction – transfer of charge does NOT require contact. This is the
natural “flow” of charge between two objects that are not touching.
4) Polarization – no charge is actually transferred it is just
rearranged/separated within a neutral object.
Charge-Force Law (a.k.a. Law of Charges): Similar charges will repel
each other while opposite charges attract.
You will use this law to determine the DIRECTION of a force on a
given charged particle.
Video
Balloons on
strings
For example in the picture below two electrons are placed near one another. The
direction of the force on electron A is to the left because it is being repelled by
electron B. The direction of the force on electron B is to the right because it is
being repelled by electron A.
neg
neg
A
B
For example in the picture below a proton and electron are placed near one
another. The direction of the force on charge A is to the right because it is
attracted to charge B. The direction of the force on charge B is to the left because
it is attracted to charge A.
pos
neg
A
B
Conservation of Charge: the net charge on an isolated system remains
constant.
Example: A system consists of two charged metal spheres. Sphere A has a charge of 20μC and
sphere B has a charge of 10μC. If the charges are brought into contact with each other, what is
the resulting charge on each sphere?
Example: A system consists of two charged metal spheres. Sphere A has a charge of 20μC and
sphere B has a charge of -10μC. If the charges are brought into contact with each other, what is
the resulting charge on each sphere?
Homework 1
Electric Charge
1) An object becomes charged. If the net charge on the object is 20μC determine:
a) if the object gained or lost electrons to become charged.
b) how many electrons were gained or lost.
c) the mass of the electrons that were transferred.
2) If 200mg of electrons are transferred onto a balloon determine:
a) how many electrons were transferred.
b) the resulting charge on the balloon.
3) Two objects are initially charged to qA = -10μC and qB = 7μC. If the objects are
allowed to touch, what is the resulting charge on each object?
II. Coulomb’s Law
Coulomb’s Law allows us to determine the (electric) force between two charged particles.
The magnitude of the force with which charges attract or repel is given by Coulomb’s Law.
The direction of this force is given by the charge force law.
Coulomb’s Law – there is a mutual force (of attraction or repulsion) between
ANY two charges which is directly proportional to the product of the charges
and inversely proportional to the distance* between the charges squared.
*The distance is the center-to-center distance
F
kq1 q 2
r2
where k is the constant of proportionality (Coulomb’s constant)
k = 9.0 x 109
Nm 2
C2
NOTES:
 According to Newton’s 3rd law the forces are equal (in magnitude) and
opposite (in direction)
 DO NOT use the sign of the charge in the calculation
 If there are more than two charges, you can only analyze the force
between two of them at a time. You would then combine all of the
forces (for each pair of charges) using your rules for vectors.
You may have noticed that this is very similar (in concept) to Newton’s Universal Law of Gravitation
Newton’s Law of Gravitation
There is a mutual force of attraction
between ANY two masses which is
directly proportional to the product of
the masses and inversely proportional to
the distance between their centers
squared.
F
Gm1m2
r2
The gravitational force is a field force
meaning it can act without direct contact.
Coulomb’s Law of Electrostatic Forces
There is a mutual force (of attraction or
repulsion) between ANY two charges
which is directly proportional to the
product of the charges and inversely
proportional to the distance between their
centers squared.
F
kq1 q 2
r2
The electrostatic force is a field force
meaning it can act without direct contact.
Example:
A small piece of plastic has a charge of +6.0μC. It is placed 12.0-cm away from another piece of plastic which carries a charge
of -4.0μC.
a) What is the electric force between the plastics?
b) Did the first piece of plastic gain or lose electrons to
become charged? How many electrons did it gain or lose?
c) How much mass did the first piece of plastic gain/lose as
a result of the transfer of electrons?
Example:
For the collection of charges shown below, what is the NET force on charge 2?
Let q1 = 5μC, q2 = 10μC and q3 = -15μC
q1
q2
q3
Example:
Consider the charges shown below. Assuming that they are fixed in position determine:
q1
q2
a) Where (w/r/t charge 1) could an electron be placed in order to have it in static equilibrium?
b) If you place a proton in the system rather than an electron, where (w/r/t charge 1) should it be placed to be in
static equilibrium?
III. Electric Field (E)
Field (E) is NOT the same as Force (F)
BUT
Field (E) is related to Force (F)
Think about Gravitational Forces and
Fields…
Electric Fields (E)
We know that two masses will exert equal
and opposite forces on each other. So an
We know that two charges will exert
equal and opposite forces on each other.
apple near the surface of the earth exerts a force on
the earth and the earth exerts an equal/opposite force
on the apple.
So an electron placed near a proton will exert a
force on the proton and the proton exerts an
equal/opposite force on the electron.
Any object near the Earth (or any other
object will mass) will experience a
gravitational force due to the Earth’s
Gravitational Field.
This field is an indication of the
RELATIVE strength/magnitude of
the force that exists between it
(Earth) and another mass.
You can think of the field as the
physical effect of a mass on the space
surrounding it.
Field is due to a single mass whereas
Force is due to a pair of masses.
A gravitational field is created
by any one mass, however, a
second mass will experience a
force when placed in this field.
ANY object (charged) placed near a source
charge (Q) will experience a force due to
the electric field.
 The field (E) exists due to a
source charge
Demo – Van de Graff
 A charge placed in this field will
experience a force
Demo – ball and Van de Graff
You cannot detect the field until
another (test) charge is placed in
it, although the field exists
without the second charge.
 Electric Field (E) is the ratio of
the force on a test charge to the
magnitude of the charge itself.
E
F
q
E
kQ
r2
IV. Electric field Lines
Electric Field Lines are a graphical way to visualize an electric field.
Based on how a proton (or other positive charge) would react when placed in the field.
The Rules:
1) Field lines are drawn away from positive
charges and toward negative charges.
2) The closer together the field lines, the
stronger the field.
3) The number of field lines indicates the
relative charge.
Example: An electric field of 260,000N/C points due west. What are the magnitude and direction of the force on a proton
at this location?
b) What are the magnitude and direction of the force on an electron?
Example:
Draw the electric field lines around an isolated positive charge.
Draw the electric field lines around an isolated system made up of one electron and one proton.
Draw the electric field lines around an isolated system made up of two protons.
Example 3
Two charges are arranged as shown.
a)
What is the electric field due to
the positive charge at point P?
+6μC
-9μC
P
25.0cm
b)
What is the net electric field due
at point P?
c)
Where would the net field be zero?
Special Information
Electric Field and Conductors
Insulators
Conductors
Semiconductors
Superconductors
For a static, isolated system:
1) Any excess charge placed on an isolated conductor resides entirely on the surface of the
conductor. This is due to electrostatic repulsion.
2) The (net) electric field inside a charged conductor is ZERO.
Faraday Cage
3) The electric field at any one point at the surface of the conductor is perpendicular to the
surface.
4) Excess charge tends to accumulate at sharp points on charged conductors.