PhET Balloons and Static Electricity Simulation
Rub a balloon on a sweater, then stick it on a wall and see how induction in insulators (also known as polarization) works.
PhET Coulomb’s Law Simulation
Modify the value of two charges and their distance away from each other to see how the electric force changes.
Hello there! Welcome to lecture 22: electrostatics!
Electrostatics introduces an important new property of matter: electric charge. This property unlocks the concepts of electricity and magnetism, which we’ll be exploring in the next several lectures. This lecture will give you an understanding of what electric charges are and how they give rise to forces and electric fields. We’ll learn that charge gives rise to a property that you wouldn’t be watching this video without: voltage!
Each of the following concepts will be discussed in this video: charge, Coulomb’s law, conduction, charge distribution, induction, electric fields, and electric potential.
Electrical charge is a physical property of matter that exists due to the presence of protons and electrons in an atom. Just as mass is an important property that leads to many important phenomena in physics, charge is an important property that leads to important phenomena as well. And just as mass is conserved, charge is conserved as well. This means that the total charge in any closed system must remain constant over time.
The term electrostatics, which is the topic of this lecture, has to do with charges that do not move. We will discuss all of the fascinating properties of charges that do move in our next lecture on electric circuits.
Charge has a symbol of the lowercase letter q. The units we use for charge are coulombs, which has a symbol of the capital letter C.
There are two types of charges: positive charges and negative charges. Every proton has a charge of positive one, therefore, protons create positive charge in atoms and molecules. Every electron has a charge of negative one. Electrons create negative charges. In a material or object that is neutral, the number of positive charges is exactly equal to the number of negative charges.
Because there are two types of charges, there are two possible interactions that the charges can experience. Two like charges (positive and positive, or negative and negative) will repel. That is, if I hold two like charges together, they will experience a force that causes them to move apart from each other. Two unlike charges (positive and negative) will attract. Therefore, if I hold two unlike charges apart from each other, they will experience a force that causes them to come together. The strength of this force will be discussed in a few minutes.
We can visualize the effect of this force by looking at how charges interact on a low-friction turntable. Two acrylic rods are rubbed with paper. This removes electrons, causing a positive charge. When one of the rods is free to rotate, and the other rod is held nearby, we can see that the first rod rotates away. Positive charges repel. Two PVC rods are rubbed with paper, this time adding electrons to the PVC, causing a negative charge. Again, the two rods held near each other causes the one on the turntable to rotate away.
When the PVC and acrylic are held nearby, now the positive rod rotates toward the negative rod, demonstrating a force of attraction between the unlike charges.
When I place a charged rod close to a neutral object: in this case, a wooden meter stick resting on a pivot, we can see that the meter stick experiences an attractive force with the charged rod. When I place the charged rod above the meter stick, the meter stick rotates upward toward the charged rod. Both positively and negatively charged rods create an attractive force with neutral objects.
How can we create positive and negative charges? We know that atoms have a positively charged nucleus comprised of protons and neutrons, and that electrons orbit the nucleus. It is very complicated to add or remove protons from an atom. It requires a nuclear process such as radioactive decay, fission, or fusion. Therefore, to create a positive or negative charge, we need to add or remove electrons from an atom. Because electrons orbit the nucleus, it is much simpler to add or remove electrons than to add or remove protons.
An ion with a charge of negative two has that charge because it has two excess electrons. An ion with a charge of positive three has that charge because it has three fewer electrons than protons. We’ll discuss how we can get electrons to move around in a later section of this lecture, but for now it’s important to realize that the charge of an object can be changed by moving electrons around.
If I hold two like-charged particles near each other, they will move away from each other when I let go. If they start at rest, and move away from each other, that means the two charges will speed up, indicating that an acceleration is present. From Newton’s second law, we know that when there’s acceleration, there’s a net force. Charged particles exert forces on each other.
Coulomb’s law is the equation that quantifies the force that exists between particles. The equation is F equals k q-one, q-two divided by d-squared. That is to say, the force equals a constant k times the charge of one of the particles, times the charge of the second particle, divided by the distance between the two particles, squared. The units of force, as always, are newtons.
The constant k is known as Coulomb’s constant and has a value of nine times ten to the nine newton meters-squared per coulomb squared.
Note the similarities with the equation for gravitational force! Both forces have a constant term, a multiplication of the two physical properties (mass for gravity, charge for electrostatic force), and are divided by the distance squared. This means that electrostatic force, just like gravity, obeys the inverse square law. Halving the distance between two charges will quadruple the force between them.
Gravitational force and electrostatic force also have some big differences. One of the biggest differences is that the electrostatic force is so much stronger than gravity. Coulomb’s constant is twenty powers of ten larger than the universal gravitational constant! Maybe you’ve noticed this if you’ve ever stuck a balloon to the wall after rubbing it in your hair. The force from a few charged particles on the balloon is easily able to overcome gravity. This also happens when small pieces of plastic stick to your hands. They’re not defying gravity: electrical charge that’s built up on the plastic will cause it to have an electrostatic force with any neutral object nearby.
The second big difference between the electrostatic force and gravity is that electrostatic forces come in two types: attractive and repulsive. There are two types of charge, and that means the force can go in one of two directions: toward and away. Meanwhile, gravity is only an attractive force. Mass can only be positive, not negative, so we will only ever experience attractive forces with other objects of mass.
When using Coulomb’s law, we need to be careful to ensure that the sign we obtain in our force calculation is consistent with the direction of that force. Recall from lecture two that vectors pointing to the right are positive, and vectors pointing to the left are negative. Vectors pointing up are positive, and vectors pointing down are negative. We will want to ensure that the direction of force corresponds with this convention.
Therefore, when calculating an electrostatic force, first calculate the magnitude of that force by using the equation. Once you’ve finished calculating the magnitude, look at the types of charges involved to determine the direction. Let’s do some examples!
Let’s say we have a charge of positive 10 microcoulombs (that is: 10 times 10 to the negative 6 coulombs) that’s 0.2 meters apart from a charge of negative 5 microcoulombs (5 times 10 to the negative 6 coulombs). What is the force that charge B causes on charge A?
First, we’ll calculate the magnitude by ignoring the signs of the charges and using Coulomb’s law. F equals k q-one q-two divided by d-squared. Multiply 9 times ten to the 9 with 10 times 10 to the negative 6 and 5 times ten to the negative 6. Then divide by 0.2, squared. The magnitude of the resulting force is 11.25 newtons.
Now we must analyze the situation to determine the direction of the force. Because B is causing the force, we consider that A is the charge that is moving as a result. Which direction will charge A move? Because the force is attractive (there are unlike charges involved), charge A will move to the right. This means our force is positive 11.25 newtons.
What is the force that charge A causes on charge B? We can solve this in two ways. The first is to see that the magnitude using Coulomb’s law will be the same, and because now B is in motion, it moves to the left, indicating a force of negative 11.25 newtons. Or we can recall from Newton’s third law that these are action-reaction pairs, meaning the forces will be equal and opposite.
Materials can be characterized by how easily they allow electrons to move around. We looked at a similar property when we learned about heat transfer in lecture 16. In fact, materials that are good at moving heat around also tend to be good at moving electrons around. We call materials in which electrons can easily move around electrical conductors. If you think about what wires are made of, maybe you can think of the type of materials that make good electrical conductors. That’s right, metal! In metals, electrons are very easily able to move around. This means we use them in all of our electric circuits: from power lines to the charging cable you use for your electronic devices.
Materials that are not good electrical conductors are called insulators. Plastic, paper, air, wood: these are all good electrical insulators. In these materials, electrons are very tightly bound to the nucleus of their atoms. Very pure water is actually a very good insulator. However, when water contains impurities such as salt, then it becomes a much better conductor.
Some materials are somewhere in between a conductor and an insulator. Their electrons aren’t super tightly bound to the nucleus as with insulators, but they’re also not as freely flowing as with conductors. We call these materials semiconductors. Silicon is probably the most widely known elemental semiconductor. It’s used in just about every integrated circuit in every computer and electronic device. Semiconductors are so great because they can be turned into an electrical switch that turns on (acts like a conductor) or off (acts like an insulator) by applying something called voltage. These electrical switches are called transistors. The computer or phone you’re watching this video on likely has many billions of these transistors inside of its processor.
Another fascinating type of material is called a superconductor. Superconductors are materials that are capable of allowing electrons to flow with no resistance whatsoever, that is, no energy will be lost to heat when electrons move about in these materials. Superconductors are generally made from certain elements or ceramic materials that are cooled down to just a few Kelvin. That is, only a few degrees above absolute zero!
If you’ve ever had an MRI, then you’ve benefitted from technology that uses superconductors. Superconducting electromagnets are used in MRI machines. They are cooled to a low temperature using liquid helium, causing a rhythmic pumping sound in the background as the MRI machine runs.
Charge distribution refers to how charges distribute themselves or move around in different materials. In metals, electrons are able to move about freely. This means that when electrons are introduced into a metal they can move around to reduce the effect of the repulsion between each individual electron. The same situation occurs when electrons are removed from a conductor. Electrons redistribute to cause the least amount of energy due to the repulsive forces between positive charged ions.
We can see this in an electroscope. When electrons are introduced into the electroscope, which is made of metal, the free piece of metal in the electroscope moves away. Because the negative charges have distributed themselves throughout the conducting material, we can see the repulsive force cause the free piece of metal to rotate to get as far away from the surrounding negatively charged metal as possible.
The same thing occurs when electrons are removed from the electroscope. The conducting material of the electroscope becomes positively charged and the repulsive force causes the free piece of metal to rotate away from the rest of the positively charged metal.
Conduction occurs whenever two or more conducting materials come into contact with each other. Charge is freely able to flow between the conductors, causing the electrons to move in such a way to minimize repulsive forces. We will discuss the effects of conduction much more in the next lecture when we talk about electric circuits. The flow of charge, current, causes many interesting electrical properties and plays a large role in our 21st century lives.
Grounding is a special type of conduction where charges redistribute themselves to an area that can accept lots of charges without causing a large buildup of electrons or positive ions. The Earth is a great ground source. Because the Earth is so large, it can accept a lot of electrons without causing a buildup of charge. When you plug in your electronics, a copper wire, or plumbing that goes into the Earth, acts as a ground connection to the Earth.
Sometimes, grounding can occur through our bodies. Humans are relatively good conductors. When I touch the electroscope, charges move around to the ground through my hand and my skin. We can see that I have discharged the electroscope, as the freely moving piece has rotated back to its equilibrium position. There is no longer a charge on the metal causing a repulsive force. As long as there isn’t too much charge flowing through a person when they act as a conduit to ground, this can be safe. This becomes very dangerous when the flow of charge becomes too high.
When I hold onto a van de Graff generator, electrons build up on my skin and hairs. After a time, we can visually see the effect of this charge buildup as my hairs begin to separate from each other: they are experiencing the force of electrostatic repulsion. The hair on my head and on my skin will stick up.
When I stick my finger out, a corona discharge emanates from my finger. This is caused by the air around my finger becoming ionized. If I amplify the audio from this demo recording, perhaps you can hear the staticky sound. This is a similar sound to something you would hear in the vicinity of large transmission lines.
Note that a LOT of electric charge transfers to my body when I touch the van de Graff generator. As long as I do not let that charge flow rapidly away from me, this is perfectly safe. I stand on a giant plastic block when I do this so that charge cannot flow through my feet into the floor. I am surrounded by insulators. The van de Graff generator would be dangerous if I were to touch an object and cause the electrons to flow through my body. The movement of charges, known as current, which will be discussed in the next lecture, is where the danger lies. Perhaps you can recall being shocked while touching a doorknob after walking around on carpeted floor in the winter. This shock does not come from the charge buildup but from the movement of charge when it is able to discharge from your body.
We can see this discharge using a Wimshurst machine. Rotating the machine causes a buildup of charge on one of the spheres. As long as the charge remains surrounded by insulators, it will remain on the metal sphere. As soon as a second sphere comes close enough, the charge will discharge, even through the gap of air in between the two spheres! I had to film this demo with the lights off to make the sparks easier to see.
In insulating materials, charges cannot move around freely. Charges will tend to stay where they are placed. When rubbing a balloon in my hair, electrons are transferred to the balloon. Because the balloon is made of an insulating material, the electrons are unable to redistribute around the entire balloon. Only the portion of the balloon that was rubbed against my hair is able to stick to the wall. The other side of the balloon does not have a buildup of electrons and remains neutral. This side of the balloon will not stick to the wall.
Induction is another way that charges can be caused to redistribute themselves in different materials. Unlike conduction, induction does not always require physical contact between objects to cause charges to move.
We can see how charges redistribute when I hold a negatively charged rod close to the top of the electroscope. It’s not touching any of the metal contacts, but we can see from the movement of the metal that charges are moving around in the electroscope. Electrostatic repulsion causes electrons to move to the bottom of the electroscope, to be as far away from the negatively charged rod as possible. While the net charge on the electroscope is still zero, there is an overall polarization of the metal. The abundance of negative charges in the bottom of the electroscope causes repulsion, and the movable piece rotates as a result of that force.
When the charged rod is moved away from the electroscope, the effect goes away.
The same effect occurs with a positively charged rod. When holding it close to the top of the electroscope, the electrons experience an attractive force, causing them to move to the top of the electroscope. This creates a build-up of positive charge in the bottom of the electroscope, causing the moveable piece to rotate as a result of the repulsion between these positive charges.
If we want to use this effect to cause a more permanent charge in metals, we can use two pieces of metal instead of one. Placing a negatively charged object nearby two touching metal objects will cause the charges in the metal to redistribute. Repulsion causes the electrons in the metal to move as far away from the charged object as possible. As a result, the metal closest to the charged object will now contain a positive charge. If the two metal objects are now separated, and the charged object moves away, we are left with two charged pieces of metal. This process is known as charging by induction.
Induction can also occur in insulators, but the effect is slightly different due to the fact that electrons cannot move around freely in insulators. If we could look at the arrangement of the molecules surrounding the balloon sticking to the wall, we would see that while the electrons cannot move, the molecules will become polarized. In effect, the molecules re-orient themselves so that the negatively charged parts of the molecules are as far from the balloon’s negative charges as possible.
These explanations of induction in metals and insulators explains a phenomenon we saw earlier in this video: that charged objects are attracted to neutral objects.
Just as we saw in our lecture on gravity, fields are a model that allow us to see how objects in the presences of forces will interact. An electric field shows us how charged objects will interact as a result of electrostatic forces. We can draw an electric field by showing how a positively charged object would move as a result of being in the presence of another charged object.
In the simplest case, we can draw the electric fields corresponding to single point charges. The first scenario is a positive charge. Say I have a single positive charge oriented in space. The drawing of the electric field will show which direction a positively charged object would go. Because of the force of repulsion, a positive object would move away from the charge. The arrows depicted on the field point away as a result. If I have a single negative charge oriented in space, the arrows will point toward that charge. This is because a positive charge will be attracted to, and move toward, that negative charge.
Electric field diagrams can be drawn for more complicated arrangements of charges, and serve as a useful model for us to determine how positive charges would move in these scenarios. And exactly as the gravitational forces are strongest when the gravitational field shows arrows being closest together, the electrostatic forces are strongest when the electric field arrows are closest together.
Just as objects of mass in the presence of a gravitational field have gravitational potential energy, charged objects in the presence of an electric field have electric potential energy. This stored energy can be used to do useful work: charge your cellphone, turn on your lights, or run your refrigerator. We can use EPE as the symbol for electric potential energy. The units, because it is a form of energy, are Joules. The equation for electric potential energy is EPE equals k times q-one times q-two divided by d. K is coulomb’s constant, q are the values of both charges, and d is the distance between both charges. This describes the energy stored as the result of holding two charges a distance d apart from each other.
Even if I did not have two charges, the presence of a single charge causes the potential, the possibility, to create energy. There doesn’t have to be a second, or third, or fourth, charge around to interact with the electric field caused by the first one. This concept of potential is very important in electronics. This is called electric potential, and a difference in electric potential between two points is known as voltage. Voltage will be a topic of lecture 23, when we discuss electric circuits.
Thanks for taking the time to learn about electrostatics! Until next time, stay well.