Hello everybody, my name is Iman. Welcome back to my YouTube channel. Today we're going to be continuing MCAT physics prep and today's chapter is all about electrostatics and magnetism. Here we're going to cover the following objectives.
We will first discuss charges. We're also going to compare and contrast insulators and conductors. Next we'll discuss Coulomb's law and define electric field. This is going to be followed up with a discussion on electrical potential energy. Our fourth objective is then electrical potential, not to be confused with our third objective.
And then we're going to cover and consider some special cases of electrostatic. So this is going to include equipotential lines and electric dipoles. And last but not least, we're going to discuss magnetism.
So we're going to define and discuss magnetic fields and forces. Now to sort of motivate this chapter, let's consider this. The word electricity, it may evoke an image of complex modern technology, lights, motors, electronics, computers, but the electric force plays an even deeper role in our lives.
According to atomic theory, electric force is the force that makes us move. forces between atoms and molecules hold them together to form liquids and solids, and electric forces are also involved in the metabolic processes that occur within our bodies. And so as we discuss this chapter and as we start, it's important we define design the first word in our title, which is electrostatics, right? Electrostatics is the study of stationary charges and the forces that are created by and which act upon these charges. Without electrical charge, we wouldn't be able to do many of the activities that we enjoy or even consider essential to living.
And so with that, let's get started and discuss our first objective charges. Is all electric charge the same or is there more than one type? In fact, there are two types of electrical charges.
We have positive charge and we have negative charge. Each type of charge repels the same type, but it will attract. the opposite type.
All right. So what that means is unlike charges attract and like charges repel. All right. Now this naming of positive and negative charge, it was arbitrarily made by Benjamin Franklin. And Franklin argued that whenever a certain amount of charge is produced on one object, an equal amount of that opposite type of charge is produced on another object.
And so the positive and negative are to be treated algebraically. So during any process, the net change in the amount of charge produced is zero. And this is essentially an example of a law that is now well established, which is the law of conservation of electric charge, which states that the net amount of electric charge produced in any process is zero or said another way no net electric charge can be created or destroyed and so if one object or a region of space acquires a positive charge then an equal amount of negative charge will be found in neighboring areas or objects no violations have ever been found and this conservation law is as firmly established as those for energy and momentum now really only within the past century has it become clear that an understanding of electricity really originates inside the atom itself. A simplified model of an atom shows that it has a tiny but heavy positively charged nucleus, and it's surrounded by one or more negatively charged electrons. The nucleus contains protons, which are positively charged.
and neutrons, which have no net electric charge. All the protons and all electrons have exactly the same magnitude of electric charge, but their signs are opposite. So neutral atoms having no net charge contain equal numbers of protons and neutrons. Sometimes an electron may lose one or more of its electrons, or it may gain some extra electrons, in which case it'll have either a negative net positive or a... negative charge and is therefore called an ion.
Now, when an object is neutral, it contains equal amounts of positive and negative charge. The charging of a solid object by rubbing, that can be explained by the transfer of electrons from one object to another. All right.
So when a plastic ruler becomes negatively charged by, um, rubbing with, say, some sort of like paper towel or something, then the transfer of electrons from the paper towel to the plastic leaves the towel with a positive charge in magnitude compared to the negative charge that's going to be acquired by. like the plastic ruler or something. Now normally when objects are charged by rubbing, they hold their charge only for a limited time.
They eventually return to their neutral state. But then the question arises, where does that charge go? And usually the charge will leak off onto water molecules in the air, and that's because water molecules are polar, right? That is, even though they are neutral, their charge is not necessarily distributed uniformly.
anyways, something that's important considering how much discussion we're having about charge, the SI unit for charge. The SI unit for charge is the Coulomb, all right, is the Coulomb. Now we have said that protons have a positive charge, electrons have a negative charge. Both protons and electrons possess the fundamental unit of charge, and that is what's written here, 1.6 times 10 to the minus 19 coulombs.
Remember that opposite charges exert attraction and like charges exert repulsive forces. All right. With that, we can also begin to discuss insulators and conductors.
All right. Something that we're going to need to have a conversation about is the difference between these two. Now, a conductor is a material that is going to allow electrons to flow freely through it, making it useful really for carrying electric charge or electric current.
An insulator, on the other hand, is a material that resists the flow of electrons, so it doesn't allow electric current to pass through it. And we can visualize that here. So this is an example of an insulator. Actually, I know a better way of doing it.
This is an example of an insulator, all right? It does not distribute charge over the surface, but notice how conductors will, all right? So that is our first objective.
We introduce the idea... idea of charge and conductors and insulators. Let me give you the takeaway points here, all right?
The takeaway points are the SI unit of charge is the coulomb. Protons have a positive charge, electrons have a negative charge, but both protons and electrons possess the fundamental unit of charge, which is that E equals 1.6 times 10 to the minus 19 coulombs. Protons and electrons also have different mass, keep that in mind, all right?
Another important thing, opposite charges exert attractive. forces like charges exert repulsive forces. All right. And the last two things, conductors allow the free and uniform passage of electrons when charged, whereas insulators, they resist the movement and charge.
and will have localized area of charge that do not distribute over the surface of the material. With that, now we can confidently move into the second objective where we will begin discussing Coulomb's law. We have seen that an electric charge exerts a force of attraction or repulsion on other electric charges.
What factors can affect that magnitude of the force? Well, to find an answer, French physicist Charles Coulomb actually investigated electric forces in the 1980s and the result was the following expression that we see here all right that is known as Coulomb's law Coulomb was able to argue that the force one tiny charged object exerts on its second tiny charged object is gonna be directly proportional to the charge of each of them. So what that means is if the charge on either one of the objects is doubled, the force is doubled. And if the charge on both of the objects is doubled, then the force increases four times the original value. This was the case where the distance between the two charges remained the same and only the charge was adjusted.
What about the distance? If the distance between them was allowed to increase, he found that the force decreased with the the square of the distance between them. So what that means is if he doubled the distance, the force fell to one fourth of its original value.
And so Coulomb concluded that the force of one small charged object exerts on a second one is proportional to the product of the magnitude of the charge on one times the magnitude of the charge on the other. And that was inversely proportional to this square distance. the square of the distance r between them. And so we get the following expression.
Again here, remember the SI unit for charge is Coulomb, charge is quantized. All right. All right. Awesome. Now, another important thing.
All right. I want to just restate Coulomb's law in maybe a slightly different way. Okay. Coulomb's law is going to essentially describe the force between two charges when they're at rest.
Additional forces will come into play when charges are in motion, but that's going to be discussed much later on. And your knowledge of that is that you need to have for the MCAT very, very limited. All right.
That's why in this objective, we're discussing charges at rest, hence the study of electrostatics, all right? And Coulomb's law gives us the electrostatic force. All right, so here we have Coulomb's equation, all right?
F here is the magnitude of the electrostatic force. K is Coulomb's constant, all right? It's equal to 8.99 times 10 to the 9 Newton times the meter squared over Coulomb squared.
Q1 and Q2, R are the magnitudes of the two charges, and R is the distance between them. All right. Now, Coulomb's constant, all right, also called the electrostatic constant, is a number that depends on the units used in the equation. All right.
So sometimes K can equal 1 over 4 pi epsilon naught. All right. And here epsilon naught has a value as well.
It is 8 point. I should write this down. Oh, right here. Beautiful.
All right. I do have it written down. 8.85 times 10 to the minus 12 Coulomb squared over Newton times meter squared. All right. But this is the traditional form of Coulomb's law.
All right. You don't need to be memorizing. I think mostly from my understanding, you will usually be given K in any problem.
But just in case, I suppose it's always better to be safe than sorry. So it's a good thing to commit to memory. Now the direction of the force can be obtained. by remembering right that unlike charges attract and like charges repel and the force always points along the line connecting the center of the two charges okay let's do a quick problem okay this problem says A positive charge is attracted to a negative charge a certain distance away. The charges are then moved so that they are separated by twice the distance.
So they start with some distance and then they're separated twice by twice the distance. How has the force of attraction changed between them? All right.
Based off of Coulomb's law. All right. Let's write this down.
Q1, Q2, R squared. Coulomb's law states that the force between two charges varies as the inverse of the square of the distance between. between them so if the distance is doubled then the force is reduced to one fourth of what it is. All right.
So for example, I don't know why I wrote D. Let's put R so that it makes more sense. All right. Let's say the distance between them goes from R to 2R. What do you think is going to happen to the force?
Well, if you plug in 2R and you square this, all right, and then K, Q1, Q2 stays the same. How does this change compared to this? This is R squared. This is going to become 4R squared. So now you've introduced this one over four factor.
Okay, and so the forest when you double the distance the force is going to be reduced by 1 4th of what it was originally All right 1 4th of what it was originally awesome now That is Coulomb's Law. Let's talk about electric field, all right? Many common forces are going to be referred to, maybe referred to as contact forces.
Like for example, if your hands are pushing or pulling a cart, or if a tennis... racket, hits the tennis ball. Those are all contact forces.
Things are touching each other and exerting some sort of force. In contrast, both the gravitational force and the electrical force, they act over a distance. There is a force between two objects even when the objects are not touching, right? The idea of a force acting at a distance was actually really, really difficult for early thinkers, right? Newton himself felt kind of uneasy with this idea when he published his law of universal gravitation.
But a helpful way to look at this situation uses the idea of fields, which was developed by the British scientist Michael Faraday. In the electrical case, according to Faraday, an electric field extends outward from every charge and it permeates all of space. If a second charge is placed near the first charge, it feels a force exerted by the electric field that is already there. Now we can in principle investigate the electric field surrounding a charge or a group of charge by measuring the force on a small positive test charge at rest. Alright, so then with all that being said, let us properly define electric field.
Every electric charge sets up a surrounding electric field, just like any mass creates a gravitational field. Electric fields make their presence known by exerting forces on other charges that move into the space of field. Whether the force exerted through the electric field is attractive or repulsive depends on whether the stationary test charge and the stationary source charge are opposite charges or like charges.
The magnitude of the electric field can be calculated in one of two ways, both of which are expressed here. All right. Electric field is equal to the force over charge.
Or we can write that the electric field is equal to KQ over R squared. And remember, K can be also equal to one over four pi epsilon naught, or it's called permittance. of free space, okay, QR.
And you can actually solve for force if you have electric field and charge by just rearranging this equation right here to solve for charge. All right, E is electric field, F is... the magnitude of the force. Q is the source charge. K is the electrostatic constant.
R is the distance between the charges. All right. Now, also note that the electric field is a vector quantity.
Now, something else that's important here to discuss since we're talking about electric field are field lines. Since the electric field is a vector, it's sometimes referred to as a vector field. And to visualize the electric field, we can draw a series of lines to indicate the direction of the electric field at various points in space.
These electric field lines are drawn so that they indicate the direction of the force due to the given field on a positive test charge. Now we can draw the line so that the number of lines starting on a positive charge or ending on a negative charge is proportional to the magnitude of the charge. So notice that near the charge, that near the charge where the electric field is greater, the lines are closer together.
All right. So, for example, here are electric field lines drawn. Right.
As a positive test charge. All right. Electric fields are pointing.
away, all right, negative charge, electric fields are pointing in, right, because the way that we draw these lines, all right, are drawn so they indicate the direction of the force that's due to a given field on a positive test charge, all right. If this was, if we were comparing this, this was a plus one charge and this was a plus two charge, we would notice more of these field lines drawn to properly display that comparison of varying charge. All right, so that's a general rule of the electric lines.
The closer together the lines are, the stronger the electric field in the region. All right, and notice that near the charge where the electric field is greater, the lines are closer together. Okay, field lines can be drawn so that the number of lines crossed unit area perpendicular to the, or perpendicular to, is proportional to the magnitude of the electric field.
And we can actually summarize the properties of the field lines here, all right? Three really important points. One, electric field lines indicate the direction of the electric field. The field points in the direction tangent to the field line at any point. Second, lines are drawn so that the magnitude of the electric field is proportional to the number of lines crossing unit area perpendicular to the lines.
The closer the lines are together, the stronger the field. And three, electric field lines start on positive charges, end on negative charges. And the number starting or ending is proportional to the magnitude of the electric field. the charge.
Also note that field lines never cross. Why not? Because the electric field cannot have two directions at the same point, nor exert more than one force on a test charge. All right, fantastic. So that is our objective two.
Let me summarize it in a couple of points, all right, because there was a lot here. Coulomb's law, we talked about it. It gives the magnitude of the electrostatic force vector between two charges.
The force vector always points along the line. connecting the center of the two charges. Next, every charge generates an electric field, which can exert forces on other charges. All right, the electric field is the ratio of the force that's exerted on a test charge to the magnitude of that charge.
And we talked about We talked about electric field vectors can be represented as field lines that radiate outward from positive source charges and radiate inward to negative source charges. Positive charges will move in the direction of the field line. Negative charges will move in the direction opposite of the field line.
All right. And those are all the important points we've discussed in this second objective. That means we can move into our third objective, electrical potential energy. All right. We.
We have already defined potential energy before. We said potential energy, stored energy that can be used to do something or make something happen. And there are different types of potential energy.
Gravitational, elastic, chemical. All right, and now this fourth form that we're going to be talking about, electrical potential energy. So similar to gravitational potential energy, this is a form of potential energy that is dependent on the relative position of one charge.
charge with respect to another charge or to a collection of charges. Electrical potential energy is given by the equation shown here, all right? U equals KQ, capital Q, lowercase q over R, all right? If the charges are alike, all right, if the charges are like charges, both of them are positive or both of them are negative, then the potential energy will be positive. But if the charges are opposite, one positive, one negative, then the potential energy will be negative.
Remember that work and energy, they have the same unit, the joule. All right, so we can define electric potential energy for a charge at a point in space in an electric field as the amount of work necessary to bring that charge from an infinitely far away. to that point. And because we know a few things, we know that F equals KQ1Q2R squared, and we know that work equals force distance cosine theta. If we defined as the distance R that separates the two charges and we assume the force and displacement vectors to be parallel, then what we can get is the following relationship for change in potential electrical potential energy to be equal to K Q capital Q lowercase Q over R.
All right, just shifting around, we notice how we get this relationship here. All right. Now, consider two charges, a stationary negative source charge and a stationary negative source charge. and a positive test charge that can be moved.
Because the two charges are unlike, they're different, they're going to exert attractive forces between them. And so the closer they are, the more stable they will be. Opposite charges will have negative potential energy.
And this energy will become increasingly negative as the charges are brought closer and closer together. All right. Now consider two positive charges, for example.
All right. Like charges, they're going to exert repulsive. forces and the potential energy is going to be positive here. All right.
We're going to have a positive potential energy because like charges repeal each other, repel each other, the closer they are to each other, the less stable and happy they will be. All right. All right. Remember that unlike gravitational systems, the forces of electrostatics can be either attractive or repulsive.
All right. In this case, like charges will become more stable the further away they move and different charges. Unlike charges will be more stable the closer they are together. All right. Let's do a quick practice problem.
This problem says if a charge of plus 2E and a charge of minus 3E are separated by a distance of 3. nanometers what is the potential energy of this system all right so we're going to use our good old equation for potential energy u equals k q big q little q this kind of like q1 q2 over r test charge and sample charge from the equation from the question all right we know that the charges are plus 2e and minus 3e so we can plug those in here all right and we know that r the distance between them is three nanometers. So we can go ahead and start to plug those in. We also know that K is equal to 8.99 times 10 to the nine power new in meter squared over Coulomb squared. All right. Then we're going to plug in those charges minus two plus two E plus two.
And E remember is 1.6 times 10 to the nine minus 19 Coulombs. All right. Multiplied by minus three E. All right. Same number here.
I'm not going to write it. All right. All over.
The distance, which is 3 nanometers, so 3 times 10 to the minus 9 meters. All right, if you plug this into a calculator, what you're going to get is minus 4.6 times 10 to the minus 19 joules. That is the potential energy of the system.
Fantastic. All right, with that, we can move in. to electrical potential, all right?
Electrical potential discussed here and what we just discussed, electrical potential energy, they sound the same. They sound very similar. They sound like they might be the same thing. They are not, but they are very closely related. In fact, electrical potential is defined as the ratio of the magnitude of a charge's electrical potential energy to the magnitude of the charge itself, all right?
We see that in this equation right here, all right? V equals U over Q. All right, V is the electrical potential. This is going to be measured in volts.
All right, hence V. All right, U is our electrical potential energy, and Q is our charge. Fantastic. Now, Even if there is no test charge, we can still calculate the electrical potential of a point in space in an electric field as long as we know the magnitude of the source charge and the distance from the source charge to the point in space in the field. like we see here in this equation, all right? V equals KQ over R, all right?
Now, electrical potential is a scalar quantity. Its sign is determined by the sign of the source charge. So for a positive source charge, V is positive.
But for a negative source charge, V is negative. For a collection of charges, the total electrical potential at a point in space is the scalar sum of the electrical potential due to each charge. Now, because electrical potential is inversely proportional to the distance from the source charge, a potential difference will exist between two points that are...
at different distances from the source charge. So if VA and VB are the electrical potentials at point A and point B respectively, then the potential difference between them known as the voltage is going to be VB minus VA. And from the equation for electrical potential above, we can further define potential difference as we see here.
Again, let's do some quick summarization of the two last objectives here. Electrical potential and energy is the amount of work required to bring the test charge from infinitely far away to a given position in the vicinity of a source charge. On the other hand, electrical potential is the electrical potential energy per unit charge. different points in space of an electric field surrounding a source charge will have different electric potential values all right with that we're going to end the chapter here all right in the next video we'll finish our last two objectives and then we'll follow it with some more practice problems let me know if you have any questions comments concerns down below other than that good luck happy studying and have a beautiful beautiful day future doctors