1. Electric Charge and Coulomb’s Law
AP Physics C

2. Sources of Charge
An atom has a dense, positively charged nucleus, containing positively charged protons and neutral neutrons.
The nucleus is surrounded by the much-less-massive orbiting negatively charged electrons that form an electron cloud.
Charge, like mass, is an inherent property of electrons and protons.
Electrons and protons are the basic charges in ordinary matter.
An object is charged if it has an unequal number of protons and electrons.
Most macroscopic objects have an equal number of protons and electrons. Such objects are electrically neutral.
Objects gain a positive charge not by gaining protons, but by losing electrons.
Protons are extremely tightly bound within the nucleus, but electrons are bound much more loosely.

3. Charges of Particles The symbol for charge is “q”
The unit is the Coulomb (C), named after Charles Coulomb
If we are talking about a single charged particle such as 1 electron or 1 proton we are referring to an elementary charge and often use, e , to symbolize this.

4. Conservation of Charge
Charge cannot be created or destroyed, only transferred from one object to another. Even though these 2 charges attract initially, they repel after touching. Notice the NET charge stays the same.

5. Insulators and Conductors
The electrons in an insulator are tightly bound to the positive nuclei and are not free to move around.
Charging an insulator may leave a patch of molecular ions on the surface, but the patches are immobile.
In metals, the outer electrons (valence electrons) are weakly bound to the nuclei.
They are detached from their parent nuclei and are free to wander through the entire solid, creating a sea of electrons permeating an array of positively charged ion cores.

6. Charging By Friction
This involves taking two objects and rubbing them together; electrons will be “ripped” off one of the materials by the other, leaving one material positively charged and the other negatively charged.
The more electronegative of the two materials gets the electrons.
This type of charging is referred to as the triboelectric effect.
This is what happens when you rub a balloon on your hair and it becomes charged.
Charging by friction is the method of charging that we experience the most in our everyday life.

7. Methods of Charging - Conduction
Another relatively simple method of charging is conduction.
Conduction is the act of taking two conductors that carry different charges and placing them in contact.
While in contact with one another, charge freely flows from one material to the other (again, assuming the materials are conductors).
The flow of charge stops once the objects have the same charge.

8. Methods of Charging - Induction
Induction is the more complicated method of charging due to its procedural nature.
To charge something through induction, you need to bring a charged object towards a neutral object, but not place them in contact with each other.
The neutral object “feels” the charged object’s presence, which polarizes the neutral object.
From there you can give the polarized charges somewhere to go, generally the Earth or another conducting object.
Eventually, this leaves you with multiple charged objects.
The Earth can be considered a giant conductor, which is why charge flows freely to or from it.

9. Methods of Charging - Induction
Induction can also be done without using the Earth as a ground.
In the diagram below, charge flows from one conducting sphere to the other.

10. Methods of Charging - Induction
Induction is the more complicated method of charging due to its procedural nature.
To charge something through induction, you need to bring a charged object towards a neutral object, but not place them in contact with each other.
The neutral object “feels” the charged object’s presence, which polarizes the neutral object.
From there you can give the polarized charges somewhere to go, generally the Earth or another conducting object.
Eventually, this leaves you with multiple charged objects.

11. Coulomb’s Law
We know that like charges repel and opposite charges attract. In addition, we have just seen how charge can be “pushed” from one object to another or within an object. There must be a force here!
Coulomb’s law describes the attritional or repulsive force that exists between charges:
𝐹 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 =𝑘 𝑞 1 𝑞 2 𝑟 2 𝑘=𝐶𝑜𝑢𝑙𝑜𝑚𝑏 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡=9× 𝑁 𝑚 2 / 𝐶 2
This force behaves very similarly to a force that we have already seen before… Gravity! Both forces are inversely proportional to the square of the distance between them.
𝐹 𝐺𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 =−𝐺 𝑚 1 𝑚 2 𝑟 2

12. Permittivity Constant
We can make many future equations easier to use if we rewrite Coulomb’s law in a somewhat more complicated way.
Let’s define a new constant, called the permittivity of free space:
𝜀 𝑜 =𝑃𝑒𝑟𝑚𝑎𝑡𝑖𝑣𝑖𝑡𝑦 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑘= 1 4𝜋 𝜀 𝑜
Rewriting Coulomb’s law in terms of this new constant gives us:
𝐹=𝑘 𝑞 1 𝑞 2 𝑟 2 = 1 4𝜋 𝜀 𝑜 𝑞 1 𝑞 2 𝑟 2
This way of writing things will make it easier when we use Gauss’ Law and potentials.

13. Coulomb’s Law
The negative on the force of gravity implies that it is a “binding” force, meaning that it is attractive.
Notice in Coulomb’s Law that if one of the charges is negative, the force becomes negative, making it attractive. Two positive charges would then create a positive force, making it repulsive.
Generally we will just be concerned with calculating the magnitude of the electric force. We can add the direction by simply stating whether it is attractive or repulsive.
If there are more than two charges present, you can use the principle of superposition to find the force on each charge.
𝐹 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 =𝑘 𝑞 1 𝑞 2 𝑟 2

14. Example
The charge of sphere 2 is twice that of sphere 1. Which vector below shows the force of 2 on 1?

15. Example
Which of the three right-hand charges experiences the largest force (there could be a tie)?

16. Example
Point charge A has a charge of –1.0 nC, and point charge B has a charge of 4.0 nC. They are separated by 1.0 cm. What are the magnitude and direction of the electric forces on charges A and B?

17. Example
Which is the direction of the net force on the charge at the top?

18. Example
Two weights of mass m = 0.25 kg are attached to separate strings of length L = 0.4 m and hung from a common point on the ceiling. When a charge "q" is placed on each mass, the masses repulse and swing out away from one another forming an angle of 22 degrees. What is the charge q?