physics 2112 unit 1: coulomb’s law today’s concepts: a) coulomb’s law b) superposition unit 1,...
TRANSCRIPT
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Physics 2112 Unit 1: Coulomb’s Law
Today’s Concepts:
A) Coulomb’s Law
B) Superposition
Unit 1, Slide 1
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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?!
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Electric Charges
Electric charges is conserved
Unit 1, Slide 3
At Fermilab
-1 +1
anti-proton proton
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Electric Charges
Tribo-electric Series
Unit 1, Slide 4
Tend to lose electrons when rubbed
Tend to gain electrons when rubbed
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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
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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
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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.
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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
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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?
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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?
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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:
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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
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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
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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
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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
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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?
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Charge on a Conductor
Unit 1, Slide 17
Charges are free to move on conductor
++
+ ++
+
+
+
+
+
+
+
+
+
+
+
Charges always on very edge of conductor