Post on 04-Feb-2022
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 -
Like sign charges repel, Opposite sign charges
attract.
Electric charge is “quantized”.
qe=1.602 X 10-19C
Charge of electron is exactly same as charge of
proton
Unit 1, Slide 2
Why?
Why?
Why?
How?!
Electric Charges
Electric charges is conserved
Unit 1, Slide 3
At Fermilab
-1 +1
anti-proton proton
Electric Charges
Tribo-electric
Series
Unit 1, Slide 4
Tend to lose electrons
when rubbed
Tend to gain electrons
when rubbed
When we place near the positively charged
glass rod, the ruler was attracted to it.
What will happen when it is placed near the
charged PVC rod?
A. It will be attracted to it
B. It will be repelled by it
C. There will be no effect
QUESTION
In our simulation, we have now rubbed the
sweater and the balloon, transferring charge
from one to the other. Both are pretty good
insulators. What can we say about the force
between the sweater and the balloon?
A. They will attract each other.
B. They will repel each other.
C. There will be no force between
them.
QUESTION
In our simulation, we have now rubbed the sweater
and the balloon, transferring charge from one to the
other, but the wall remained neutral. All three are
pretty good insulators. What can we say about the
force between the wall and the balloon?
A. They will attract each other.
B. They will repel each other.
C. There will be no force between them.
QUESTION
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 8
The force on a charge due to another charge is proportional to the product of the charges and inversely proportional to the separation squared.
r
The force is always parallel to a line connecting the charges, but the direction depends on the signs of the charges:
q2
q2 q1
q1
Like signs repel
Electro-static Force
q2 q1
Opposite signs attractq2 q1
Unit 1, Slide 9
2
21
r
qqF
Coulomb’s Law
Electricity & Magnetism Lecture 1, Slide 10
2,12
2,1
212,1 r̂
r
qqkF
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.
Example 1.1 (Force on charge)
Electricity & Magnetism Lecture 1, Slide 11
2
2,12
2,1
212,1 r̂
r
qkqF
-30uC+25uC
q3q1
2m
2m
What is the electro-static force on q3?
25X10-6 kg30 X10-6 kg
What is the gravitational force on q3?
A hydrogen atom is composed of a nucleus containing a single
proton, about which a single electron orbits. When the electron
is in the lowest orbital position, the electric force between the
two particles is 2.3 X 1039 greater than the gravitational force!
How would we adjust the separation between the two particles
so the electric and gravitational forces are equal?
A) We must move the particles farther apart.
B) We must move the particles closer together.
C) It can’t be done at any distance.
QUESTION
Example 1.2 (forces between students)
Unit 1, Slide 13
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?
Question
Unit 1, Slide 14
Which weight is closest to the approximate force between those paperclips (recall that weight = mg, g = 9.8 m/s2)?
A) Paperclip (1 g x g)
B) Text book (1 kg x g)
C) Truck (104 kg x g)
D) Aircraft carrier (108 kg x g)
E) Mt. Everest (1013 kg x g)
k 9 x 109 N m2 / C2
electron charge 1.6 x 10-19 Coulombs
NA 6.02 x 1023
Two 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.
122
12
21 r̂r
qqkF
CheckPoint: Forces on Two Charges
Electricity & Magnetism Lecture 1, Slide 15
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:
CheckPoint Results: Forces on Two Charges
Electricity & Magnetism Lecture 1, Slide 16
A) Since they are both positive they have to repel each other, and I would think the one with the stronger charge would repel more.
B) Just like a fly having the same amount of force impact on a bus that the bus has on the fly, two charges will have equal and opposite effects on each other in accordance with Newton's Third Law.
C) the big charge is going to really want to push away the smaller charge, therefore the vector for the smaller "mass" is larger than on the larger "mass".
q1
q2
q3
q4
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:
F2,1
F3,1
F4,1
F1
Superposition
Electricity & Magnetism Lecture 1, Slide 17
F2,1
F3,1
F4,1
F1
1F
...1,41,31,2 FFF
What happens to the magnitude of Force on q1 if its sign is changed?
A) |F1| increases
B) |F1| remains the same
C) |F1| decreases
D) Need more information to determine
Electricity & Magnetism Lecture 1, Slide 18
Question: Superposition
q1
q2
q3
q4
The direction of all forces changes by 180o – the magnitudes stay the same:
F2,1
F3,1
F4,1
F1
F2,1
F3,1
F4,1
F1
F2,1
F3,1
F4,1
F1
q1
q2
q3
q4
F2,1
F3,1
F4,1
F1
q1
q2
q3
q4
Electricity & Magnetism Lecture 1, Slide 19
1F
...1,41,31,2 FFF
1F
- ...1,41,31,2 ---- FFF
Electricity & Magnetism Lecture 1, Slide 20
-Q Q
Case 1 Case 2
Compare the magnitude of the net force on q in the two cases.
A) |F1 | > |F2|
B) |F1 |< |F2|
C) |F1 | |F2|
C) D) Depends on sign of q
CheckPoint: Compare Forces
Case 1 Case 2
Electricity & Magnetism Lecture 1, Slide 21
-Q Q
Case 1 Case 2
F1
F2 0
CheckPoint: Compare Forces
A) No matter the sign of charge q, there will be an attractive and repulsive force in case
1 (same direction), and two forces (attractive or repulsive depending on the sign of the
charge on q) that cancel so that the net force on q is zero.
B) the bigger force exerted on q is case 2 because the net force exerted in case 1 is 0.
C) Although Case one will be repelled and two will be attracted, the magnitude of the
forces will be the same
D) I believe that if the sign of q is negative, the force on q will be less than if the sign of q
is positive, as there will be two repelling forces acting on it rather than one repelling
and one attracting force.
Electricity & Magnetism Lecture 1, Slide 22
-Q Q
Case 1 Case 2
F1
F2 0
CheckPoint: Compare Forces
D) because if the central charge is neutral there is no net force on either. If
the central charge isnt neutral, the net force would be greater in case 1.
Good point. From now on, if I refer to a q, you can assume |q| = 0
Example 1.3 (Force on charge)
Electricity & Magnetism Lecture 1, Slide 23
2
2,12
2,1
212,1 r̂
r
qkqF
q2
-30uC
+10uC
+25uC
q3q1
2m
2m
What is the force on q2?
Charge on a Conductor
Unit 1, Slide 24
Charges are free to move
on conductor
++
+ ++
+
+
+
+
+
+
+
+
+
+
+
Charges always on very
edge of conductor