Electric charge and electric force

0:00- [Instructor] When you push against a wall, you feel the wall pushing back, and we call that the contact force, right? But what's interesting is that the atoms of your fingers are not literally touching the atoms of the wall, like, you know, solid balls touching each other.

0:16Instead, what you're feeling as contact is actually an electromagnetic repulsion, this propulsion between electrons of your fingers and the walls, which is pretty awesome if you think about it. And guess where this repulsion comes from? It comes from a fundamental property of matter called charge.

0:33So let's explore charge in a little bit more detail. So what exactly is charge? It's a fundamental property of matter. Just like how mass is a fundamental property which produces gravitational force, charge is a fundamental property that is responsible for electromagnetic force.

0:50Today, we don't think of electricity and magnetism as separate phenomena. Instead, we model them as a single force, electromagnetic force. But in this video, let's learn how to model electric forces. Eventually we'll learn how to model magnetic forces and eventually we'll unify them later on.

1:07Okay, so a few things about charge. Charge is a scalar quantity, which means it only has magnitude and no direction, which is pretty awesome. That means you can just add them up, you don't have to worry about vectors. And what do you think is the unit of charge?

1:19Well, it's coulombs, named after Charles Coulomb, who did a lot of work on this. And so the symbol we use is a capital C. But wait a second. If charge is such a fundamental property of matter, why do electric forces not seem obvious in our everyday life? Well, to answer that, let's zoom into matter.

1:39We know that matter is fundamentally made of atoms and we know atoms have a nucleus at the core surrounded by an electron cloud. Now, this diagram is definitely not to scale, but what's important is that charges come in two flavors, positive and negative. The protons have a positive charge and the electrons have an equal amount of negative charge.

2:00And since neutral atoms have equal number of protons and electrons, the total charge on a neutral atom becomes zero, meaning they are electrically neutral, and most matter, which is made of these neutral atoms, are also electrically neutral. And that's why the electric effects are not so apparent in our daily life.

2:19But if we can create a charge imbalance, like, for example, when you rub a balloon with your hair, (instructor chuckling) then you can see electric forces in action. We'll talk about that later on. But how much charge does an electron or a proton have? Well, the magnitude of the charge on a single proton or an electron is equal to this number exactly.

2:43We call this number e, the elementary charge. And what's interesting is that this is an exact value because we define coulombs this way. By definition, the charge on an electron or a charge on a proton is exactly this number. But why did we settle on this exact number for the definition?

3:06Well, that's got something to do with the history. We'll not worry too much about it. But for most practical purposes, we'll just round this off to 1.60 times 10 to the -19 coulomb. And so the charge on electron is -e, and the charge of the proton is +e. And of course, neutrons are neutral, they have zero charge.

3:28And since electrons and protons are fundamental particles, this is the most fundamental charge we can think about. This is the most elementary charge, the smallest charge that matter can have. Now, of course, according to today's model, protons and neutrons can be further divided into smaller particles called quarks, and they can have a fraction of this charge, but let's not worry about that.

3:52For our purposes, let's just consider this as the smallest possible charge. Okay, so now that we know what a charge is, how do we model the forces that charges exert on each other? Well, we do that using something called the Coulomb's law. The law states that if you have two point charges separated by some distance r, then the electric force they exert on each other is proportional to the magnitude of the charge, and inversely proportional to the square of the distance between them.

4:25Okay, so first of all, notice that when we're talking about the magnitude of the force that they exert on each other, we don't have to worry about the signs, whether we're dealing with positive or negative signs. That doesn't matter. What matters is the magnitude of the product of the charges.

4:40And secondly, notice that there's an inverse square relationship, that's why it's also called an inverse square law, which means if you double the distance between the charges, the force becomes not 1/2, but 1/2 squared, 1/4. And if you triple it, the force becomes 1/9, and so on.

5:01And remember that Coulomb's law is applicable when we're dealing with point charges, meaning their sizes are much, much smaller compared to the distance between them. Okay, but this looks a little familiar, right? Including the name inverse square law. It feels like we've heard that before, right?

5:18Yes, we have! When it comes to gravity, the Newton's law of universal gravity is analogous to this. A force of attraction between any two masses is proportional to the product of the masses, and inversely proportional to the square of the distance between them.

5:35But there's an important difference between the two. Gravity is always attractive. So the force of attraction is always along the line joining them, but what's important is that it's always attractive. Electric force can be attractive or repulsive. If you're dealing with like charges, which mean they have the same, you know, signs, then the force will be repulsive.

5:58If you are dealing with unlike charges, then the force will be attractive. But again, here, the force will always be along the line joining them. Anyways, the proportionality constant over here is G, the gravitational constant, and it has this specific value. Similarly, the proportionality constant over here is K, which we call the Coulomb's constant, and its value is roughly this much.

6:22And can you pause the video and work out its units quickly? Okay, well, we just have to rearrange to isolate K, and when you do that, you get Newton meter squared divide by Coulomb squared. But what's interesting is that Coulomb's constant is often written this way, one over four pi epsilon naught.

6:44Why? Because epsilon naught is an important constant. It's called the vacuum permittivity or permittivity of free space. And it's a constant that we'll see everywhere in electricity and magnetism, and that's why it makes sense to write this in terms of epsilon naught.

7:02And its value happens to be this much. Okay, but why's it called permittivity? Well, it's actually got a lot of history and we'll not dive deep into it. What's important for us is that it's a physical constant, an important one. And when you plug this number over here, the value of the Coulomb's constant pops out to be this much roughly.

7:26But notice how we call it the vacuum permittivity, or the word permittivity of free space. That's because that is the value for that constant when the space between the charges is vacuum. But what if we have some material medium, meaning some type of matter in between these charges?

7:43Then the medium will have its own permittivity value, which is greater than this vacuum permittivity. But why? Well, if you put some medium in between, and let's say these atoms represent the atoms of that particular medium, the positive is the nucleus, the charge in the nucleus, and the negative is the electron cloud.

8:01Now, this negative charge will repel this electron cloud away from it, and it'll pull the positive nucleus towards it. So it'll make the molecules stretch out. We call this phenomenon electric polarization. We say that the charges are polarized. Now, this is an oversimplification because the charges are also affected by this particular charge.

8:24But what's important is that these polarized atoms exert additional electric forces on q1 and q2, and that affects the magnitude of the net forces on the particles. But don't worry too much about this right now. We will explore electric fields in matter in more detail later on.

8:40The key point over here is the Coulomb's force is affected by the medium. And of course, if you were to compare the electric force between any two particles with the gravitational force between them, the electric force will be orders of magnitude larger than the gravitational force.

8:57At astronomical scales, large objects are pretty much electrically neutral, and so the dominating force is that of gravity. But at very tiny scales within the atoms, when you consider molecules, it's the electric force that dominates and therefore we completely ignore gravitational interactions between them.

9:16But the final question we could have is what happens if there are more than two charges? How do we deal with Coulomb's, how do we use Coulomb's law? Well, let's take a concrete example. We have three charges at the corners of an equilateral triangle. Let's say we want to calculate the force on this particular charge, charge at C.

9:35How do we do that? The trick is, first, you only calculate the force on C due to, say, B and ignore all other charges. The direction of this force will be repulsive along the line joining them, and the magnitude of this force, we'll just call this as force of B on C, that's given by the Coulomb's law.

9:52So it's going to be K times the product, which is Q-squared divided by R squared, and R over here is just length L. Next, you calculate the force on C due to only A, ignoring everything else. This time the force is attractive because we have unlike charges. And the magnitude of this force is going to be K times, the product this time is 2Q squared, so it's gonna be 2KQ square divide by L square.

10:22And, of course, if there were more charges, then you keep continuing the process. The idea is you calculate the forces separately, and then to calculate the total force on this charge Q, you add them up vectorially. This principle is called the principle of superposition.

10:42So let's add these two vectors. Well, since this force is twice as this, well, let's just call this force as F and then this will be 2F. And so here we have 2F and this will be F. And so now how do we add these two vectors? Well, we can decompose this vector into vertical and horizontal components, and then we can add the horizontal and the vertical separately.

11:04It'd be a great idea to pause the video and see if you can do this yourself. Okay, so let's decompose it into horizontal and vertical. How do we figure out these values? Well, we know this angle to be 60 degrees because this is an equilateral triangle. And so this component will be the sine component, it's the opposite side.

11:20So this will be 2F sine 60, and this component will be 2F cos 60. Sine 60 is root 3/2 and cos 60 is 1/2, so the two cancels. And look, this component also happens to be F, which is exactly equal and opposite to this one. So those cancel out. And so look, this is the only component that survives, which means this is the net force on C.

11:44So that's going to be F root three. So the net force on C is going to be F root three, which is basically root three times KQ squared or L squared. And this net force points directly upwards.