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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
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
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
q1Like signs repel
Electro-static Force
q2 q1
Opposite signs attractq2 q1
Unit 1, Slide 6
221
r
qqF
Coulomb’s Law
Electricity & Magnetism Lecture 1, Slide 7
22,12
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.
Coulomb’s Law
Electricity & Magnetism Lecture 1, Slide 8
22,12
2,1
212,1 r̂
r
qkqF
2,1F
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).
q2q1 2,1r
If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direction of r12 (left).
q1 q22,1F
2,1r
Our notation:
is the force by 1 on 2 (think “by-on ”) is the unit vector that points from 1 to 2. 2,1F
12r̂
Example 1.1 (forces between paper clips)
Unit 1, Slide 9
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?
Example 1.2 (forces between students)
Unit 1, Slide 10
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?
CheckPoint: Forces on Two Charges
Electricity & Magnetism Lecture 1, Slide 11
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:
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 12
F2,1
F3,1
F4,1
F1
1F
...1,41,31,2 FFF
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
F1F2,1
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 13
1F
...1,41,31,2 FFF
1F
...1,41,31,2 FFF
Electricity & Magnetism Lecture 1, Slide 14
-Q +Q
+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|
D) Depends on sign of q
CheckPoint: Compare Forces
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
What is the direction of horizontal force on Q?
A) Fx > 0 B) Fx = 0 C) Fx < 0
x
y
3q
q qq
Q
Electricity & Magnetism Lecture 1, Slide 15
Example 1.3 (Force on charge)
Electricity & Magnetism Lecture 1, Slide 16
22,12
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 17
Charges are free to move on conductor
++
+ ++
+
+
+
+
+
+
+
+
+
+
+
Charges always on very edge of conductor
