Introduction
How do things interact?
Lecture 1
Electric Charge and Force
1) Gravity
- a force between masses
- holds planets in orbit, etc.
• Properties of Electric Charges
• Charging
• Coulomb’s Law
2) Electromagnetism
- a force between charges
- responsible for all familiar forces (except gravity) –
friction, normal, magnetic
3) Weak Nuclear Force
- decay of particles
4) Strong Nuclear Force
- holds nuclei together
Serway and Jewett: Ch. 23
Physics 1E03 - Lecture 1
Electric Charge
Electric Charge (continued)
• A scalar quantity
• Comes in “positive” and “negative”
+

F
• Charge appears in nature in units of “e”:
+
-
-
+
-
2
REPEL

F
eg: Particle
electron
proton
REPEL
ATTRACT
Charge
-e
+e
•Net charge is a conserved quantity: that is,
the algebraic sum of positive and negative charges
is constant.
Units: coulomb, C
and also “smallest unit of charge”, e  1.60210-19 C
Eg: +5e-3e = +2e = +8e-6e
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Concept Question 1.1:
Which of the following is true? (There may be more than one.)
a) it is not possible to determine if a single charged body is
positively or negatively charged.
b) electrostatic forces can be properly described by postulating
that like charges attract and unlike charges repel, even though
this convention is not used.
c) if the definition of “positive” and “negative” charges were
switched, then all electrostatic forces could still be properly
explained.
d) it is possible that there are three kinds of charge, “+”, “–” and
“=“, where like charges repel and unlike charges attract.
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Charging by Induction
Insulators:
charges do NOT move
eg: glass, rubber, paper
- can be charged by rubbing,
but charges do not move
Conductors:
(some) charges move freely
eg: metals, some liquids
Semiconductors:
electrical properties
between insulators and
conductors
eg: silicon, germanium
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Quiz
Charge is conserved.
The conductor is neutral (no net
charge). When a charged rod is
brought close to it (without
touching) the net force on the
conductor will be:
Experiment shows that objects acquire a net charge by the
transfer of charge from one object to another, not by the
creation of new charge on one sign.
Conductor
Charged Rod
neutral
+
+
+
+
_
+
+
_
_
_
_
A)
B)
C)
D)
_
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Coulomb’s Law
attractive
repulsive
zero
it depends whether the rod is
positive or negative
-----Conductor
Physics 1E03 - Lecture 1
Coulomb’s Law
• The electrical force between two stationary charged
particles is given by Coulomb’s Law
• The force is attractive if the charges are of
opposite sign
• The force is inversely proportional to the square of the
separation r between the particles and directed along
the line joining them
• The force is repulsive if the charges are of like
sign
• The electric force is a conservative force
• The force is proportional to the product of the
charges, q1 and q2, on the two particles
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Coulomb’s Law
Coulomb’s Law
Point charges

F
q1, q2exert forces on each other:
q2

q1
r
force due to charge 2 on
charge 1

F
rˆ
21
e
12
r̂
2
2
2
C2
q2
force due to charge 1 on
charge 2

F12
unit vector, dimensionless

r
rˆ12  12
r12


Since r21   r12 and
is a unit vector parallel to r
ke  8.988  10 9 N  m
r̂12

qq
F12  1 22 r̂12
r12

qq
F k
rˆ
r
1
q1

F21
12

r12


r21  r12 ,
Direction of the force is
along the line joining the
point charges.


F21   F12
(Coulomb’s constant)
Physics 1E03 - Lecture 1
This agrees with Newton’s third law.
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Coulomb’s Law
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Exercise:
GIVEN:
• Remember the charges need to be in coulombs
L
 e is the smallest unit of charge
• except quarks
30 30
m
 e = 1.6 x 10-19 C
q
 So 1 C needs 6.24 x 1018 electrons or protons
L
•Identical Masses, m=1.0 gram
(equilibrium)
m
q
•Equal charges q
•L= 60 cm
FIND: q
• Typical charges can be in the µC range
 µC (micro coulomb) = 10-6 C
• Remember that force is a vector quantity
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Exercise:
Quiz:
m=1.0 g, L= 60 cm, q=q1= q2 =?
What happens to each angle if
the charge on the left is doubled,
and the other one is halved?
Assume mass of charges is small.
Draw Free body diagram:
L
y
m
T
30o
Fe
? L
2q
Ty
Tx
?
(equilibrium)
m
q/2
x
A) angle increases
B) angle decreases
C) angle stays the same
mg
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Quiz:
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Example:
q2  20C
Two small conducting spheres have unequal charges of opposite
sign, so that they attract each other with force Fi when separated by
a distance d. They are brought into contact, and separated again by
the distance d. The force Ff between the spheres is now
a)
b)
c)
d)
e)
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300mm
400mm
zero
smaller, and still attractive
smaller but repulsive
larger, but repulsive
not enough information
q1  10 C
q3  30 C
Find: Force (vector) on q3 , in Cartesian form.
answer: F  (17 i  60 j) N
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Solution:
Fe  k
Finding Resultant force vector:
q1 q2
r2
q2  20  C
y

F31
q4  40  C
300mm
x
400mm

F32
q1  10 C
q3  30 C
Find: Force (vector) on q3 , in Cartesian form.
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Solution
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y


F34 , x
F32

F31
x

F34
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
F34 , y
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