Chapter 3 Lecture Notes



Electrostatics is the branch of physics that deals with the force exerted by a static (i.e. unchanging) electric field upon a charged object.

Positive and Negative Charge - When you rub a rubber rod on fur some of the electrons from the fur are transferred to the rubber rod. This makes the rubber rod negatively charged and the fur is positively charged.

charging contact

When you rub glass on on Asbestos (not the smartest thing to do anymore) the glass becomes negatively charged and the asbestos becomes positivley charged. However, if you rub the same glass rod on silk the silk becomes negatively charged and the glass is positively charge.


So this shows that it all depends on what is rubbed together to see what gains electrons and what loses electrons. There is a chart below that shows what happens.

Through many experiments it was discovered that charge, either electrons or protons have the same charge, except one is negative and one is positive.

Charge is quantized and conserved - Charge on an electron is charge electron and the charge on a proton is charge proton

Video on Charge


Laws of Electrostatics

1. Repulsion-Attraction: Like charges repel and unlike charges attract.

law one law one


2. Inverse Square Law: Law of electrostatics that states the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

inverse square

Formula for an Inverse Square Law: inverse

Example 1

In this example we will use the Inverse Square Law to find an unknown quantity.

Inverse Square Law

Now for the pieces that we know in this example:

example 1 quantities

We are given the intensities on the light in candela's. Light is used in this example because it also behaves with an inverse square law. In this example we need to find distance for the second place the light is placed. So, now we plug in the quantities in the corresponding places in the formula and solve for the distance.

example 1 formula

example 1 formula

Example 1 Answer



Coulomb's Law - Charles Coulomb developed an experiment to find the force that charged particles exert on each other. He suspended a thin rod with a metal ball by a very thing string. He calculated how much force is needed to twist the rod a certain number of degrees. Then he brought a charged sphere close and measured the twist in the string.

coulomb apparatus

When he analyzed the data he figured out Coulomb's Law.

coulomb law

where k is coulomb's constant coulomb constant, q are the charge on the objects and d is the distance from center to center between the objects.


Video on Coulomb's Law


Example 2

You place two small charge spheres 10 cm apart with a force of 5 N between them, but you only know what one of the charges. Find the charge on the second sphere. First, the numbers:

Example 2 Numbers

Now we put the numbers in Coulomb's Law formula with the constant.

coulomb's law

example 2 formula

Now we need to solve for the unknown charge. We multiply by the distance squared and then divide by the constant and the known charge.

example 2 solution



3. Distribution: Law of Electrostatics that states charges reside on the surface of conductors but are evenly distributed throughout nonconductors.



4. Concentration: Law of Electrostatics that states the greatest intensity of charge will be on the surface where the curvature is the sharpest.

concentrationsharp points


5. Movement: Law of Electrostatics that states only negative charges move along solid conductors.


Chapter 3 Podcast Part 1 Electrostatics


Electrification - There are different ways to charge objects. They are explained below.

Charging by Friction: Electrification that occurs when one object is rubbed against another and, due to differences in the number of electrons available on each, electrons travel from one to the other.

The Triboelectric Sequence
Asbestos On contact between any two substances shown in the column, the one appearing above becomes positively charged and the one below becomes negatively charged.
Fur (Rabbit)
Fur (Cat)
Human Skin
Copper, Brass
India Rubber




Charging by Contact: Electrification by contact occurs when two objects come in contact so that charges can move from one object to the other so the charges are distributed evenly between the objects.

contact contact


Static Discharge: The result of electrons jumping the gap between two objects, one negatively charged and one positively charged, resulting in the equalization of the charges of the two objects. This is also called a spark or lightning if it is big enough.




Charging by Induction: Induction charging is a method used to charge an object without actually touching the object to any other charged object. Induction is the process of electric fields acting on one another without contact.


To charge by induction you bring a charge object close to another object and then ground the object being charged. After the ground is removed the original charge object is removed and the second object is charged opposite of the original.



This is a molecule level diagram of charging by induction. It shows that the negatively charged electrons are forced away from the negatively charge rod.





Electric Fields

Electric Fields: A field extending outward in all directions from a charged particle, such as a proton or an electron. The electric field determines the electric force exerted by the particle on all other charged particles in the universe; the strength of the electric field decreases with increasing distance from the charge according to an inverse-square law.


Electric Field Movie




Electric Current: A flow of electrons through a conductor, the size of the current is proportional to the rate of electron flow. Measured in coulomb per second or ampere (A).



Conductor: Something that allows electricity to flow through it easily. Water and most metals are good conductors. Conductors can allow electricity to flow through them because the electrons in their atoms move between atoms very easily.


Insulator: Something that does not allow electricity to flow through it easily. Glass and special rubber are good insulators. Insulators do not allow electricity to flow through them easily because the electrons in their atoms do not move easily from atom to atom.


Semiconductor: A material whose electrical resistance can be switched between insulating and conducting. Silicon is the most commonly used semiconductor material and the basic material for building most chips.


Superconductor: a substance whose electrical resistance essentially disappears at temperatures near absolute zero. A commonly used superconductor in magnetic resonance imaging system magnets is niobiumtitanium, embedded in a copper matrix to help protect the superconductor from quenching.



Current Flow

Conventional Current: Conventional current is the direction the positive charges would flow if they were able to flow.


Direct Current: Electric current in which electrons are flowing in one direction only.


Alternating Current: Electric current that reverses direction, usually many times per second. Most electrical generators produce alternating current.


Potential Difference: Work which must be done against electrical forces to move a unit charge from one point to the other, also known as electromotive force (EMF). Measured in volts (V). volt = joule per coulomb


Resistance: Electrical resistance is a measure of the degree to which a body opposes the passage of an electric current. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.


This diagram shows how the connection between the valence band and the conduction band is closest in a conductor. This means that a conductor has valence electrons that are easy to move.



This diagram shows that resistance and temperature are related in conductors, semiconductors, and insulators.


When certain materials are cooled to near absolute zero their resistance decreases and then disappears. These are called superconductors.


To calculate the resistance of a material you need to know the length of the material, the permitivity of that material and the cross-sectional area. Luckily, in this class we will not have to use it except for fun.

Resistance: resistance



Ohm's Law

Ohm's Law: The relationship that exists between the electrical parameters of voltage (electrical pressure), resistance (the opposition to the voltage), and current (the flow of electrons in the circuit). Ohm's Law states that the amount of current flowing in a circuit is equal to the applied voltage divided by the circuit resistance.

ohm's law

ohm's law Triangle

This diagram shows a way to use Ohm's Law and when to multiply or divide. As part B shows - to find the resistance R you need to divide the voltage by the current.

Example 3

I have attached a 12 V battery to a circuit that has a resistance of 6 ohms. What is the current through the circuit. We will use Ohm's Law to find the answer.

ohm's law

example 3 numbers

Now we plug in the quantities and solve for the current.

example 1 formula

example 3 answer

Therefore, there are 2 A of current in this circuit.



Power: The rate at which electric energy is converted into another form, such as light, heat, or mechanical energy (or converted from another form into electric energy). Units watt(W) = joule/second



Example 4

You hook up a 36 V battery to a light bulb that draws 2 A of current. What is the power rating of the light bulb?

power formula

example 4 numbers

Now we plug the numbers into the formula.

example 4

example 4

So this bulb uses 72 watts of power.


When power is sent over high voltage power lines some of that power is lost due to resistance. We can calculate the amount of power lost using the following formula.

Power loss formula: powerloss


Example 5

There is a high voltage powerline that has an equivalent resistance of 30000 ohms and draws 100 A of current. What is the power lost in the powerline?

We will use the Power loss formula to solve this problem.

Power loss formula

example 5 numbers

Now we plug in the values.

example 5 formula

example 5 answer

Therefore, we lose this many watts of power.



Series and Parallel Circuits

Series Circuit: An electric circuit designed to send electrons through various resistance devices by linking them one after the other.

series circuit

In a Series Circuit the current is the same across each resister. The voltage drop across each resistor can be added together to equal the voltage of the battery. To calculate the equivalent resistance of a Series Circuit you add up the resistors.


Parallel Circuits: An electric circuit designed to send electrons through various resistance devices by giving each component its own branch.

parallel circuits

In a Parallel Circuit the voltage is constant and for the circuits we will see is the voltage of the battery. The current in each branch will add up to the current in the entire circuit. To calculate the equivalent resistance of the circuit you add the reciprocals of the resistors and then flip it back over.


  Series Parallel
Current Same in each element, each element same as total circuit, series current Sum of all elements equals total circuit, parallel current
Voltage Sum of all elements equals total circuit, series voltage Same in each element, each element same as total circuit, parallel voltage
Resistance Sum of all elements equals total circuits, series resistance Sum of reciprocal of each element is inversely proportional to the total, parallel resistance

Example 6

Find the current and voltage drop across each resistor in the following circuit.

Series Circuit

Now we need to find the equivalent resistance of the circuit.

example 6

example 6

example 6

Now we use Ohm's Law to find the current in the circuit.

example 6

example 6

Therefore, there are 2 A going through each resistor.

To find the voltage drop across each resistor you use Ohm's Law again.

example 6

example 6

example 6

If add the three voltage drops you get the voltage of the battery.



Example 7

Find the current and voltage across each resistor in the circuit.

parallel circuit

First we find the equivalent resistance.


example 7

example 7

example 7

Now we take the reciprocal of this to find the resistance.

example 7

Since the voltage across each resistor is the resistance of the battery (12 V) we can use Ohm's Law to find the current in each.




The sum of these will be the current in the circuit.


End of Chapter 3 Lecture Notes