1. Physics 2112 Unit 1: Coulomb’s Law
Today’s Concepts:
A) Coulomb’s Law
B) Superposition

2. 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
Why?
Why?
Why?
How?!

3. Electric charges is conserved
At Fermilab -1 +1
anti-proton
proton

4. Tribo-electric Series
Electric Charges
Tend to lose electrons when rubbed
Tribo-electric Series
Tend to gain electrons when rubbed

5. 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

6. Opposite signs attract
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 r
The force is always parallel to a line connecting the charges, but the direction depends on the signs of the charges:
Opposite signs attract q2 q1 q2 q1
Like signs repel

7. Unit of Charge is Columb (C)
Coulomb’s Law
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.

8. Coulomb’s Law Our notation: is the force by 1 on 2 (think “by-on ”)
is the unit vector that points from 1 to 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). q2 q1
If the charges have opposite sign, the force by charge 1 on charge 2 would be opposite the direction of r12 (left). q1 q2

9. 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?
F = 9e9 x (1.6e-19 * 3e22)^2 / 100 = 2 e 15 Newtons
Equivalent to weight of 2e14 kg object near surface of the earth
paperclip 1e-3 kg
textbook 1 kg
person kg
car kg
Aircraft carrier tons = 1e5 x 1e3 = 1e 8 kg
Mt Everest m height,. Estimate volume as 1/3 h^3 = 1/3 * (9e3)^3 = 243 e 9 m^3. (if density = 1000 kg/m^3) = 2.43e14 kg.

10. 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?
F = 9e9 x (1.6e-19 * 3e22)^2 / 100 = 2 e 15 Newtons
Equivalent to weight of 2e14 kg object near surface of the earth
paperclip 1e-3 kg
textbook 1 kg
person kg
car kg
Aircraft carrier tons = 1e5 x 1e3 = 1e 8 kg
Mt Everest m height,. Estimate volume as 1/3 h^3 = 1/3 * (9e3)^3 = 243 e 9 m^3. (if density = 1000 kg/m^3) = 2.43e14 kg.

11. 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:

12. 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
F2,1
F3,1
F4,1 F1
F4,1
F2,1 q1 F1
F3,1 q4 q3

13. The direction of all forces changes by 180o – the magnitudes stay the same:q1 q2 q3 q4
F2,1
F3,1
F4,1 F1 q1 q2 q3 q4
F4,1
F2,1 F1
F3,1 F1 F1
F2,1
F2,1
F3,1
F3,1
F4,1
F4,1

14. 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
Case 1
Case 2
If the CheckPoint was done before the first class, you could use this opportunity to show results. If not, the next slide (hidden) present the CheckPoint as a Clicker Question

15. 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 > B) Fx = C) Fx < 0 Q q q q

16. Example 1.3 (Force on charge)q2 2m
+10uC q1 q3
-30uC 2m
+25uC
What is the force on q2?

17. + + Charge on a Conductor Charges are free to move on conductor
Charges always on very edge of conductor