1. PHYS 219 Fall semester 2014 Lecture 02: Coulomb’s law &
Interaction of point charges
Dimitrios GIANNIOS
Physics & Astronomy Department
Purdue University

2. Electric, Magnetic phenomena and light: Electromagnetic Theory
this lecture
Charge Q
Electric field E
Electric force FE
Current I=Qv
Magnetic field B
Magnetic Force FB
F=mα

3. Observational Facts
Discovery of electricity is generally credited to the Greeks
About 2500 years ago
They observed electric charges and the forces between them in many situations
Used amber
A type of dried tree sap
After amber is rubbed with a piece of animal fur, the amber can attract small pieces of dust

4. Observational Facts, cont.
The Greek word for amber was “elektron” from which we get the words electron and electricity
Modern experiments use plastic and paper
The force occurs even when the plastic and paper are not in contact

5. Basic Properties of Charges
There are two types of electric charges
They are called positive and negative
Protons have positive charges
Electrons have negative charges
Charge comes in quantized units
All protons carry the same amount of charge, +e
All electrons carry the same amount of charge, -e

6. Basic Properties, cont.
Like charges repel each other, unlike charges attract
Like charges – both positive or both negative
Unlike charges – one positive and one negative
The “like” and “unlike” apply to the signs of the charges, not their magnitudes

7. Basic Properties, final
Charge is conserved
The total charge on an object is the sum of all the individual charges carried by the object
Charge can move from place to place, and from one object to another, but the total charge of the universe does not change

8. What is Electric Charge?
Charge is a fundamental property of matter
The amount of charge on a particle determines how the particle reacts to electric and magnetic fields
The SI unit of charge is the Coulomb
Electron charge = -e = -1.6 x C
Proton charge = +e = +1.6 x C
neutron charge = 0
symbol e: the magnitude of the charge on an electron or proton
q and Q: charge in general

9. How do objects become charged?
The addition or removal of electrons creates negatively and positively charged objects
Except under extreme conditions, protons stay in place and electrons move
What is total charge on this nanoparticle?
Ans:Qtot =3xe-=3x(-1.6x10-19 C)=-4.8x10-19 C
- = 1e- - -
+ = 1p - -
How was a net charge on this object created? + - + -

10. A fun example - + - - - + - - + - - - - - balloon Approach wall fur
- --
friction
+ - -
- + -
- - +
balloon -
- - - - +
- - + -
- - + ++
wall
Rub balloon with fur

11. Electric Forces and Coulomb’s Law
Electric force can be attractive or repulsive
Assume two charged particles can be modeled as point particles
The magnitude of the electric force between the two particles is given by Coulomb’s Law

12. Coulomb’s Law
Coulomb’s Law says the magnitude of the force between two electric charges is given by
The constant k = 9 x 109 N . m2 / C2
The direction of the force is along the line that connects the two charges
A repulsive force will give a positive value for FE
Between like charges
An attractive force will give a negative value for FE
Between unlike charges

13. Features of Coulomb’s Law
The form of Coulomb’s Law is similar to Newton’s Law of Gravity
Both laws exhibit a 1/r2 dependence on the separation between particles
A negative charge can move in a circular orbit around a positive charge
This was the early model for the atom
Gravity is always attractive
Electric forces may be attractive or repulsive

14. Features of Coulomb’s Law, cont.
The value of FE given by Coulomb’s Law is the magnitude on each of the particles
A force of FE is exerted on q1 and a force of equal magnitude and opposite direction is exerted on q2
Newton’s Third Law action-reaction pair but acting from a distance!

15. How strong is the electric force?
Assume you have two boxes, 1m apart, each containing one gram of electrons (me = 9 x gr)
There would be N=1.1 x 1027 electrons in each box:
total charge Q = N x e- ≈ x C = -108 C
This is almost a million times larger than the force between the Sun and the Earth!!!
Ordinary matter consists of approximately equal numbers of electrons and protons
With equal numbers, Qtotal = 0 and FE = 0

16. Principle of Superposition
Q: Since Coulomb’s Law only involves TWO point charges, what do you do when more than two point charges are present at one time? A: Since force is a vector, the total force exerted on a particular charge is the vector sum of all the individual forces acting on that charge. This is often called the Principle of Superposition

17. The Addition of vectors (graphical)
Total (net) Force:

18. Addition of vectors (numerical)
1. analyze each vector to its components y y θ x x
2. Add the vector components along each direction

19. Example of total force calculation
numerical input:
α = 10 cm = 0.1 m,
q1= |q2| = q3 = 1μC = 10-6 C
π/4
π/2
Step 1: Units!
π/4
Step 2:Geometry! y
Step 3: Force Diagram
45o x q3

20. Example of total force calculationy
Step 4: Vector Components
45o x
Step 5: Force Magnitude: Coulomb’s Law
Step 6: Add vector components