Physics 2112
Unit 1: Coulomb’s Law
Today’s Concepts:
A) Coulomb’s Law
B) Superposition
Unit 1, Slide 1
Electric Charges
Electric charges come in two sign: + and -
Why?
Like sign charges repel, Opposite sign charges
attract.
Why?
Electric charge is “quantized”.
qe=1.602 X 10-19C
Why?
Charge of electron is exactly same as charge of
proton
How?!
Unit 1, Slide 2
Electric Charges
Electric charges is conserved
At Fermilab
-1
anti-proton
+1
proton
Unit 1, Slide 3
Electric Charges
Tend to lose electrons
when rubbed
Tribo-electric
Series
Tend to gain electrons
when rubbed
Unit 1, Slide 4
Conductors / Insulators
Conductors – charges are free to move
anywhere on the conductor
Insulators - charges remain where they
are place except in cases of “extreme”
force
Unit 1, Slide 5
Electro-static Force
The force on a charge due to another charge is proportional to the
product of the charges and inversely proportional to the separation
squared.
q2
q1
F 
q1 q 2
r
r
2
The force is always parallel to a line connecting the charges, but the
direction depends on the signs of the charges:
q2
q1
q2
q1
q2
q1
Opposite signs attract
Like signs repel
Unit 1, Slide 6
Coulomb’s Law

q1 q 2 2
F1 , 2  k 2 rˆ1 , 2
r1 , 2
k = 9 X 109 N m2/C2
Unit of Charge is Columb (C)
(big!) qe=1.602 X 10-19C
Charles-Augustin de Coulomb – French engineer who was a pioneer in torsion and
soil mechanics.
Electricity & Magnetism Lecture 1, Slide 7
Coulomb’s Law
Our notation:

F1, 2 is the force by 1 on 2 (think “by-on ”)
rˆ12 is the unit vector that points from 1 to 2.

kq 1 q 2 2
F1 , 2 
rˆ1 , 2
2
r1 , 2
Examples:
If the charges have the same sign, the force by charge 1 on charge 2
would be in the direction of r12 (to the right).
q1

r1, 2
q2

F1, 2
If the charges have opposite sign, the force by charge 1 on charge 2
would be opposite the direction of r12 (left).

q1 F
1, 2

r1, 2
q2
Electricity & Magnetism Lecture 1, Slide 8
Example 1.1 (forces between paper clips)
Two 1 gram paperclips are separated by 10
meters. Then you remove 1 electron from each
atom on the first paperclip and place it on the
second one.
What is the force between the two clips?
Unit 1, Slide 9
Example 1.2 (forces between students)
What would the force be between two 80kg
students sitting two meters apart if the charge
of the proton were 10-10% greater than the
charge of an electron?
Unit 1, Slide 10
CheckPoint: Forces on Two Charges
Two charges q = + 1 μC and Q = +10 μC are placed near
each other as shown in the figure below.
Which of the following diagrams best depicts the forces acting
on the charges:
Electricity & Magnetism Lecture 1, Slide 11
Superposition
If there are more than two charges present, the total force on any
given charge is just the vector sum of the forces due to each of the
other charges:
q2
F1
F2,1
F4,1
F1
F3,1
q1
F3,1
F2,1
F4,1
q4
q3




F1  F2 ,1  F3 ,1  F4 ,1  ...
Electricity & Magnetism Lecture 1, Slide 12
The direction of all forces changes by 180o – the magnitudes stay the same:
q2
q2
F4,1
F4,1
F1
q1
F2,1
F1
F3,1
q3
q3
F2,1
F2,1
F3,1
q4
F1
q1
q4
F1
F2,1
F3,1
F3,1
F4,1




F1  F2 ,1  F3 ,1  F4 ,1  ...
F4,1




 F1   F2 ,1  F3 ,1  F4 ,1  ...
Electricity & Magnetism Lecture 1, Slide 13
CheckPoint: Compare Forces
Compare the magnitude of the
net force on q in the two
cases.
A) |F1 | > |F2|
B) |F1 |  |F2|
C) |F1 |< |F2|
D) Depends on sign of q
Q
Q
q
q
Q
Q
Case 1
Case 2
Electricity & Magnetism Lecture 1, Slide 14
CheckPoint: Force from Four Charges
Four charged particles are placed on
a circular ring with radius 3 m as
shown below. A particle with charge Q
is placed in the center of the ring
y
3q
x
What is the direction of horizontal
force on Q?
A) Fx > 0
B) Fx  0
Q
C) Fx < 0
q
q
q
Electricity & Magnetism Lecture 1, Slide 15
Example 1.3 (Force on charge)
q2
2m
q1
-30uC
+10uC

kq 1 q 2 2
ˆ
F1 , 2 
r
1, 2
2
r1 , 2
q3
2m
+25uC
What is the force on q2?
Electricity & Magnetism Lecture 1, Slide 16
Charge on a Conductor
Charges are free to move
on conductor
+
+
+
+
+
+
+
+
+
+
+ +
+
+
+
Charges always on very
edge of conductor
Unit 1, Slide 17
+