High School Physics Electric Force & Charge

Hi welcome back to educator.com. Today we’ll be talking about the electric force and charge.0000

Just to start off, you’re currently watching this video on some sort of computer that runs on electricity.0006

The screen is emitting light to your eyes because of electricity. The speakers are pumping out sound because of electricity.0011

The room that you’re currently in probably has lights that are run on electricity. You can probably look out your window and see street lights that are running on electricity.0018

On top of learning you almost certainly use electricity for warmth, transportation, food preparation, and storage, entertainment, communication, lighting things, and many, many other things.0027

Electricity makes up a fundamental part of our modern life. Without it we wouldn’t be able to have most of what we have and what we think of as common comforts, things that we just expect.0039

If we want to understand how all of the technology that makes up the modern world works, almost all of it we’re going to have to understand how electricity works.0051

The first step to understanding modern technology is understanding some of the basics’ behind electricity.0059

The foundation of electricity is the concept of charge. We denote charge with the letter q. Like mass charge is a fundamental characteristic of an object.0065

Also like mass, it’s deeply connected to the atomic make up of an object.0076

However, unlike mass charge comes in two opposite types. We call the two types positive charge and negative charge.0080

There’s not special reason why we call one negative and we call the other one positive. We could have chosen anything that just denoted their opposite nature.0088

We want something that’s opposite so that we remember the fact that they do come in two opposite versions.0095

It could have been anything really, it could have been anything. It doesn’t matter but it got set as positive and negative long ago by Benjamin Franklin who in addition to being one of the founding fathers, the United States of America, was also a pioneering scientist and did a huge amount of research.0101

The name suck and here we are using it today. Like charges repeal each other, so if you have two positive charges they push away from one another. Similarly if you have two negative charges, they also push away from one another.0118

However, opposite charges attract. So if you have a positive and a negative charge they attract each other.0133

This is also a little bit different than mass and gravity. When we were dealing with mass before any mass, two masses, they attract each other. There’s no repulsive version of gravity as far as we know.0139

As long as we’re going to have that we’re going to have this big difference between the way gravity works and the way electrical force works.0149

The electro static force, it’s going to work based on repulsion and attraction. It’s possible to do more than just pulling things in. It’s also possible to push things away with the electric force.0157

Before we talk more about electricity and the charge let’s talk about where the charge is coming from.0169

Let’s look at a simple model of the atom. At the center of an atom is a densely packed nucleus containing protons, which have positive charge and neutron which have no charge, neutral.0174

Pro for positive. Surrounding this nucleus is a moving cloud of electrons. Negative charge. Ele, electrical. There’s all these connections coming out.0185

What we’ve got here is we’ve got a model of the helium atom. Helium atom is atomic number 2. It’s got two protons in the middle and it’s got two electrons orbiting that nucleus in the center.0194

We’ve got the charges showing up, both in the center and the outside. A proton is much more massive than an electron but they each have the same amount of charge.0210

Even though they’re very different, one is moving, one is still, one’s massive, the other one is very not massive. They both have the same amount of charge in them.0220

But opposite types. Electrons have negative charge. Protons have positive charge.0230

Furthermore, generally atoms have the same number of electrons and protons. So they have a net charge of 0. Whenever we pull something off the periodic table we’re looking at it in general form of what it is when it has a full complement of its electrons.0236

They’re be slight changes as it can potentially gain or lose electrons. It can be disrupted; it can have this net charge of 0 but be disrupted through the gain or loss of electrons.0250

We call this ionizing. An atom can be ionized and if it’s ionized it can either loss or gain electrons, giving it a net charge.0262

If you gain electrons, you’ll be a negative ion. If you lose electrons, you’re a positive ion. Because if you lose electrons you’ll now have fewer electrons than you have protons so you’ll have less negative charge than you have positive charge and vice versa for the other direction.0272

Now we’ve got this idea of where charge is coming from. It’s possible to displace charge, we can move charge around and disrupted the starting neutrality of an object but it’s not possible to destroy charge.0288

Just like if we have an object we can pick it up and move part of it somewhere, we can scope of the dirt and we can move that dirt somewhere else but we can’t completely destroy that dirt.0300

That dirt will still be around. Just the same way with charge, we pick up some electrons, we move them somewhere else. We don’t get rid of the electrons, they get shifted.0311

Energy and momentum just like energy and momentum were we have conservation, charges always conserve.0319

When an ion is created it’s created because an electron leaves one particle and goes to another particle.0325

So we haven’t destroyed the electron, we haven’t destroyed the charge; we’ve just shifted it around. One particle will now become slightly negative and the other particle will become slightly positive by the amount of that electrons charge.0330

Just how much charge is in an electron or a proton? It’s the elementary charge. Since each one of these tiny, tiny things is where we get a charge from.0343

We know that a proton charges is equivalent to an electrons charge it’s going to be this tiny amount. They come like tiny, tiny grains of sand. Tiny grains of charge.0352

This elementary charge is 1.602 x 10^-19 coulombs where c is the letter for denoting coulomb, the unit for measuring charge.0363

Charge is measured with the coulomb. If it’s an electron we’d have a negative e, -1.602 x 10^-19 coulombs. If it were a proton it would be positive so we’ve have +1.602 x 10^-19 coulombs.0373

Notice this is a very small amount of charge. This is very small, 10^-19 is a very small, small number.0388

Since charge only comes in elementary charge chunks an object can have only an integer number of elementary charges. We can’t put on -4.7 of these charges, we can only put on 1 charge, 2 charge, 3 charge, 4 charge.0395

Or we could put on negative amounts, by putting on the negative version, an electron. We could have -1, -2, -3 e. Any of those possibilities but it is going to have to come in integer chunks of e.0410

However if we’re dealing with a large charge values such as one whole coulomb, remember an elementary charge is 10^-19, really tiny, tiny amount.0420

If we’re dealing with a large quantity of charge like say 1 whole coulomb of charge, that’s small elementary charge amount we can for the most part forget about the fact that it’s coming from this discreet nature.0431

We don’t have to worry about that chunky nature. The difference between 1 coulomb of charge and 1 coulomb plus one elementary charge is so slight we can effectively treat charge as continuous value without worrying about its chunky nature.0444

It’s like if you were to stick your hands under a water faucet. Each bit of the water is made up of a single water molecule, but because so much water is flowing, we don’t have to really treat it as if it’s a bunch of individual grains, a bunch of individual molecules bouncing off our hands.0457

We can treat it as its one collective continuous fluid quantity. So when we’re dealing with large quantities of charge, it’s okay to not worry about ‘Am I precise integer quantity?’0473

Because that is integer quantities are only going to be noticeable when we’re dealing with very small quantities of charge.0484

That said if we’re dealing with a very small quantity of charge you want to make sure that it is going to be an integer quantity of this e value.0489

If it’s not on this e value, this elementary charge value then it isn’t a possible amount because it’s got to come in these discreet chunks, otherwise it’s not possible to have it.0495

Charge is at its heart coming from either electrons or protons. It’s coming from the atomic level.0503

We know like charges repeal each other, opposite charges attract. We’ve talked about where charges are coming from.0511

But we haven’t talked about what the forces involved are. How much push do they have? How much pull do they have? What’s the strength of these forces?0517

The size of the force is given by coulombs law which is k x q1 x q2 over r squared. This force is called the electro static force.0524

The static is because it’s stationary, if we just have two objects sitting then its pushing for what they would be when we just look at statically, as opposed to flowing current charge which we will talk about later.0535

Current is the sort of thing that we’re used to in electricity that’s moving around in our walls, what we’re used to when we’re dealing with computers, when we’re dealing with electronic objects.0547

We’re used to dealing with current electricity as opposed to static electricity. Many of the same rules, pretty much all of the same rules will wind up applying. But that’s why it’s called the electro static force.0557

Because we’re just looking at what it is at one instant, how much is something pushing something else around.0566

Let’s investigate what all these letters mean. Q1 and Q2 are the charges of the objects. We have to know what the charges we’re dealing with are.0571

R is the distance between the objects, or more accurately the centers of the objects. If we’re dealing with two spheres we’re not going to look at the edges of the spheres closest, we’re going to look at the centers of those spheres.0580

For the most part we can just remember it as the distance between the objects. K is the electro static constant. This is just a special number that we have to memorize or write down or refer to.0590

K is equal to 8.99 x 10^9 Newtons times meters squared per coulomb. The reason why we’ve got…actually times over coulomb squared because what we want to make sure is that all of these things, the meters squared, they cancel out.0601

With the r squared, meters squared and r squared will cancel each other out. Similarly the coulomb squared will cancel out with q1 x q2 since they’re both in coulombs.0618

We’ll be left with something that’s just Newtons once we do all the calculations which is exactly what we want our force to come out in.0627

Finally notice this is the magnitude of the force. Remember force is still a vector. It’s up to us to point it in the correct direction. If we’ve got something…if we’ve got positive charges we need to remember that is going to be pushing away from one another.0633

If we’ve got two negative charges once again it’s going pushing away from each other. From one center to the other center, from one object to the other object, that’s the direction the force is going to move.0649

Finally, if we have a positive and a negative we can denote that with a negative force to show attract to one another. We can also just denote that in our force diagram that this is important and it can wind up screwing up some of our problems if we don’t catch that negative thing.0658

Conductors and insulators. It’s important to know how easily charge can flow through an object. Some materials hold onto their outermost electrons very loosely allowing them to pass charge around very easily.0672

Like a bucket brigade. We call such materials conductors. What I mean by a bucket brigade is we’ve each got each of these atoms. Say that for some reason there’s a force pushing electrons this way.0684

Then this electron can push into this one at which point it will get another electron pushed into this one. So another electron will get pushed into this one and so another electron will get pushed into this one.0697

So another electron will get pushed into this one. They each hand their electron up to the guy next to them. They’re able to very quickly move electrons around the surface of the material because they all simultaneously hand their electron up to the next guy next to them.0706

These electrons are freely moving so they conduct the electrons around easily. Metals in general make great conductors. Silver, copper, gold, aluminum are some of the best conductors.0720

Pretty much every metal and this is one of the things that makes a metal a metal is the fact that it is easily…easy for it to hand outermost electrons, its top level electrons around allowing it to conduct electrons around the surface of the metal very easily.0732

Or the surface of whatever conductor for [inaudible] conductors in general. On the flip slid we could be talking about an insulator. If a material holds onto its electrons very tightly, it’s very difficult for it to pass an electron around, for it to pass charge around.0748

We call such a material an insulator. Why do we call it an insulator? Because we call it insulator from when people were working on this originally, something that would insulate against the motion of charge.0762

That would keep charge from being able to move through it. This is a great thing if you’ve got copper wire with charge running through it and you want to make sure you can’t accidentally touch that copper wire and get shocked by the electrons going through you.0773

Instead you wrap an insulator around so you can now brush that copper wire and you won’t be able get shocked by it.0785

This is what those cords are where we’ve got cords that say, you want to plug in your microwave? There’s that plastic rubbery cord around it. That’s an insulator to keep you from touching the copper wires.0791

If we were to touch those copper wires we could potentially get hurt and the machine wouldn’t work if things wound up getting shorted it out.0800

So we’ve got to keep them insulated from one another to make sure that things can run smoothly and easily without accidentally connecting where they’re not supposed to connect.0806

Some great insulators include rubber, glass, air, and pure water; specifically it has to be chemically pure water. Just H2O. If salts get added, that suddenly allows the ability for electrons to be passed around.0815

One thing I’d like to point out is even though I keep saying electrons passed around; we can still look at this as the idea of positive charge being passed around.0828

Normally, the thing that’s really moving around is electrons, however if we had that bucket brigade idea. Well if everybody passes one electron to the right then at the end we’ve effectively just caused a positive to show up.0835

If everyone hands one guy to the right then the first guy to hand, who nobody hands something to him, we’ll he’s got one less electron which means he has more positive charge elementary unit.0850

He’s got one more positive charge unit…elementary charge. We can effectively move positive or negative charge around in a conductor.0860

We can treat it as if a positive thing is working just as much as a negative is moving around. In reality it’s only the electrons flowing around, but at the same time we can still treat it as if the positive is moving around.0868

From our point of view in measuring it we won’t be able to notice a difference between which specific type is moving. We’ll be able to tell if its negative or positive but we can treat it as that because there’s no way to fundamentally know which ones moving until we’ve got this atomic theory behind us.0879

That’s why Benjamin Franklin wound up naming the positive part for the protons; the thing that’s stationary is because at the time he didn’t know which one moved around and which one stayed still.0895

He just sort of accidentally bet it on the wrong horse, oh well. Conduction, if we have a conductive material, it makes it easy to pass charge around.0905

Since like charges repeal each other they want…of course they don’t actually have any real feelings in this, they’re just following basic laws of nature.0915

But we can treat it as if they’re trying to get away from each other. They want to get as far from each other as possible if they’re a like charge.0922

If a conductive object with charge on it touches around conductive material, the charge will spread out between the two things.0930

If there’s a lot of charge here, they’re trying to get away from each other but they’re stuck because they’re on a single object.0937

If they come along and they touch another object, suddenly they’ve got this other place to flee to. They’ve got more room to expand to.0942

They’ll expand onto it, they’ll conduct onto it and we’re going to have conduction onto the other material.0948

Some of the charge will leave the first object and go onto the second object. Here’s a great diagram to show this idea.0954

At beginning, we’ve got lots of negative charge on this first bar and we’ve got no charge on this second bar. The second bar has no charge on it but the first bar has a lot of negative charge on it.0962

We touch the two bars together and the electrons go “Oh man! More space to go to.” They all run over into there until they’re now all evenly distributed it.0974

The two bars are identical so they make it so that they distribute themselves evenly. If you’ve got two identical objects they’ll wind up distributing evenly because that’s the best way to be able to get as far away from each other as possible.0983

So they’ll distribute evenly over two identical objects, half of them run onto the second bar, the other half are like “Well I’m going to have at least as many neighbors were I go now, I might as well stay put.”0996

So they stay put, we separate the two bars and they’re still going to have the charges that they had in the second one because they’ve got no reason to run back onto the first one.1007

There’s no reason to get back on, they like having more room to spread out. They’re going to stay separated. This is a great example on conduction.1014

We can do a different thing though were we do induction. Similar to the idea, we’ve got this thing where the charges want something. They either want to away from each other if they’re the same or they want to be near each other if they’re the opposite.1023

That means if we’ve got charged object, if we bring that charged object near a conductor we’ll be able to induce a charge. What this means is that we assume; let’s say the conductor starts off neutral.1035

That means that it’s got positive and charges throughout. Well if we bring one type of charge over, well, all of the opposite charges are going to be like “Oh hey, let me get near you, let me get near you.”1048

They’ll all run up to it, they’ll try to get near it. All the guys who are the same as the thing that went there are going to be like “I don’t want to be near you.”1058

They’re going to run away from it and we’re going to get this separation. Some of the charge will get near the object that’s approaching and some of the charge will run away from the object that’s approaching.1065

Notice the net charge will remain the same in the object that’s the conductor, the conductor being induced. Then that charge will remain the same but the location of the charge will swirl around.1075

The conductor makes it very easy for charge to move around both positive and negative. It’s going to take that chance to be able to get as close to it or as far from the thing depending on what it once again quote on quote wants.1086

Here’s another visual example we can see, in the beginning we’ve got some negatively charged object over here and it’s far enough to not really any impact on this second object over here, the conductor.1098

We’ve got this conducting object and it’s just neutral and it’s got positive and negative charges mixed about and the negative charges don’t like each other but they like the positive charges, so things are basically pretty evenly distributed.1109

However, if we bring that negatively charged object really close to the conductor all of the sudden, all these positive guys, all these positive guys say “Hey, I want to be near to it.” They run up to the edge and they say “Let me get near it, let me get near it, let me near it.”1123

They can’t of course just jump onto it because we haven’t touched the two objects. We’re assuming that there’s some good insulator between them like air or the vacuum or something along those lines.1138

So they can’t get across to it but they can at least be near it, they’re pulled to it by the force of electricity. The positive charges are pulled to that side, at the same time the negative charges are repelled; they’re pushed away from the object.1149

They don’t want to be near it, they get pushed away in the other direction and so they’re going to be as far as they can. We’ve induced a charge, there’s’ no net charge change but in different locations of our conductor, we’re going to get different effective charges.1162

At least as long as the charged object is near the conductors. If the charged object where removed from the conductor, things would go back to being their mixed self because once again the positive don’t want to be near each other.1178

The negatives don’t want to be near other, so they’d spread out again and they’d once again mix with the other kind.1189

However, when we’ve got this super charged object moved near it things are going to break from their neutrality and they’re going to try and get near each other and they’re going to huddle up, pressing either towards it or trying to get away from it, depending.1194

Now we’re ready for some examples. An electroscope is a devise for measuring charge. It has a conducting rod that goes into a glass jar to keep out air motion, where it touches two very thin conducting plates.1210

By being in this glass jar air motion won’t be able to affect those glass plates so we know that the only thing that’s going to happen there is electrostatic force.1220

If the rod is touched by a charged object the plates will spring apart. Why?1228

Think about, if we’ve got a charged object, if we put a charged object up against this, lots of positive charge. Well some of the positive charge is going to get into it.1234

It’s a conductor so that positive charge is going to spread out as much as it can. It’s going to spread down to these plates.1245

These two plates both have positive charge. Positive charge repeal, they’re very thin, they’re very light weight and they’re going to swing up.1253

They’re going to push away from each other. What about…would it be possible to cause the plates to spring apart without actually touching the rod?1261

Would it be possible to cause the plates to swing apart without having to bring a conductor directly against it?1271

So here we’ve brought it directly against it. But we could do a similar thing where if we had a negative thing, we could induce a positive charge up here.1278

We can induce a positive charge. So all the positives will go ‘Oh hey, positive, positive, positive.’1290

We’ll get a bunch of positives up here; let’s erase this one just so we don’t have to get confused about which one we’re looking at.1295

All the positive charges, they run up there. When all the positive charges run up there, well where are the positive charges from the other place?1301

All the negative charges, they’re going to run down here. There’s going to be less positive charges down here.1311

Positive charges are going to be induced at the top without even needing to do contact. We don’t need direct conduction; we can induce the positive charge at the top.1318

Which means that we’re also going to have induced negative charge at the bottom. Once again we’ve got two kinds, opposite charges, they’re going to swing apart, they’re going to push apart from each other.1326

Second example. What’s the total positive charge in 50 grams of neutral uncharged iron, the total negative charge?1336

What’s the net charge in the iron? How much do all of the electrons in it make up for the negative charge? How much do all of the protons make up for the positive charge?1346

What would be the net charge? Well first off, we’re going to have to find out how many atoms of iron are in 50 grams.1355

We’re going to have to go to using mols. Since the atomic weight is 55.845 the number of mols, n is equal to the big mass, weight and grams divided by the atomic mass.1361

50 grams divided 55.845 and we get .895 mols. How many atoms are in a mol? The number of atoms in a mol, from before was 6.022 x 10^23 atoms per mol.1379

If you don’t remember this we talked about this in changes due to heat because we had to talk about it to get the ideal gas law across.1404

If you’re curious about understanding this more, go back; check out that section on mols. If you don’t need to know it that’s okay, you’ll still be able to get some of the idea of what’s going on here.1412

6.022 x 10^23 atoms per mol. If we want to know how many atoms we’ve got, we multiply these two together.1422

.895 x 6.022 x 10^23, that will tell us how many atoms of iron we have. So that gives us 5.39 x 10^23 atoms of iron.1430

The iron symbol is fe. So we know we’ve got 5.39 x 10^23 atoms of iron. In each one of these atoms there’s so number of protons and there is some number of electrons.1451

If the whole thing is neutrally charged then we know that we’re going to have to the same number of electrons in both….every atoms is going to have the same number of electrons as does protons.1462

What’s the number have to be? The atomic number is 26. We know it’s got 26 protons, 26 electrons for a neutrally charged one.1472

If we want to find out how many protons there are we take that 26 and we multiply it by that 5.39 x 10^23 number of atoms and that means since each atom has 26 protons we’re going to have a total number of protons of 1.4 x 10^25 protons.1482

We’re going to do the exact same operation to figure out the number of electrons. So 1.4 x 10^25 electrons.1505

Now we know how many electrons are running around in there, how many protons are running around in there.1514

How much charge does one proton have? How much charge does one electron have? Remember elementary charge is 1.602 x 10^-19 coulombs.1520

That’s a very small amount but we’ve got a whole bunch of protons. If we want to know what the positive charge is, it’s going to be that elementary charge times the number of protons we’ve got.1534

We’re going to have a positive charge from our protons of 2.24 x 10^6 coulombs. For our electrons we’re going to get the exact same thing.1547

Elementary charge times the number of electrons, same number of electrons except, is the elementary charge positive or negative now?1563

Remember we’re dealing with electrons so we’ve got negative charge. We’re going to get -2.24 x 10^6 coulombs.1568

Now we haven’t dealt much with electric forces yet but I’ll have you know, that is a huge amount of charge, like a terrifying amount of charge.1578

One coulomb is actually a lot of charge. One kilogram really, really common, we’re used to 1 kilogram in everyday things.1586

One coulomb charge just sitting static on an object, that’s a lot, lot of charge. It’s something you could potentially get but it’s a lot of charge.1592

10^6 coulombs is a gigantic amount and that’s just in 50 grams of iron. The important thing to note is that it’s 10^6 coulombs but there’s also it’s paired opposite. -2.24, so we’ve got positive and negative, so we’ve got it cancelled out.1603

The net charge is 0 coulombs. Since we’ve got neutral iron atoms, we know that we’ve got to have the same number of protons, same number of electrons.1620

So for every one of them they’re going to cancel each other out for the net charge. We’ve got massive positive charge and we’ve got massive negative charge, the total of each one is really, really large but when we look at it on the whole, we get this cancellation.1635

It’s just like when you’re sitting on a chair, you’ve got fairly large force pushing down on you, fairly large force pushing up on you, but in the end nothing really happens because you’re in static equilibrium.1647

Same thing going on in each one of these atoms at the same thing going on over the 50 grams as a whole. There’s this massive amount of charge there, massive potential forces going on, but because they’re intermixed they have no net effect and so the net charge cancels out as 0.1658

Two point masses in deep space. What the means is that they’re not going to be affected by any other forces than one another.1674

The first object has a mass of 4.7 x 10^6 kilograms and it has a charge -8.01 x 10^-12 coulombs. Not very much charge on it, but it’s a fairly massive object.1681

Second object has a pretty small mass, 100 kilograms. If the two objects are in static equilibrium what must be the charge q2 on the second object?1694

First thing to notice, what are the two…what forces are acting on this?1705

We’ve got two objects in deep space. Every object with a mass exerts gravitation pull on other massive objects.1711

We’ve got the force of gravity first. What’s the force of gravity? Force of gravity, magnitude for force of gravity is g x m1m2 / r², distance squared.1718

What else is there? Well we’ve got charge on one of them and we know that they’re in static equilibrium so we’ve got to have some other force canceling out that gravitation pull between them.1731

So we’ve got to have the electric force also here. Magnitude of the electric force is equal to k x q1q2 over that distance squared once again.1739

We’ve know that since f, the force of gravity and the force of electricity must be pushing in opposite directions and they have to be equal.1752

We know that the force of gravity, force of gravity is pulling in on both of them but there’s also has to be a force of electricity pushing out by the same amount.1761

Ultimately we’re going to have a cancellation of forces. If we’re going to get cancellation of forces that means that those two things must be equal.1773

If these two things are equal, what are we going to get out of it? We’ve got g m1 m2 / r² = k q1q2 / r².1783

Well first thing turns out we don’t need to know the distance. So if you’re worried that we didn’t know the distance, don’t worry about it. We can cancel out because it shows up on both sides.1799

At this point if we want to solve for q2 we just set q2 on one side. Q2 equals g m1 m2 / k q1.1806

At this point we need to remember what’s the gravitation constant? We go and we look it up in a manual or if we’re on a test hopefully we’ve memorized it or hopefully your teachers nice and lets you look up that thing, which I think is perfectly reasonable, but some teachers don’t.1819

6.67 x 10^-11. Then k, electrostatic constant is 8.99 x 10^9. We plug in all the numbers we have; 6.67 x 10^-11.1832

The mass of the first object is 4.7 x 10^6 times that 100 kilograms divided by 8.99 x 10^9 for k times that first charge, -8.01 x 10^-12.1851

If that gets a little bit hard to see but it will ultimately give us once we solve the whole thing out, but we’re going to get -0.435 coulombs.1875

What about the fact that we’ve got a negative number here? Should that worry us? No, not at all, we want a negative number.1887

If we hadn’t gotten a negative number we’d know something would have gone wrong. Because we know gravity has to be pulling together and for us to get a repulsive force from electricity we know that first object has a negative charge, the second has to have a negative charge.1893

Otherwise we won’t have that repulsive force. If we don’t have a repulsive force we’re not going to be able to cancel out the attractive force of gravity.1905

We’re able to find out that the charge has to be negative and then we can work it out and we get -0.435 coulombs.1912

Final example. We’ve got two identical metal spheres fixed in place, one here and another one here. At first they have an attractive force on each other of .15 Newtons.1919

We’re going to assume gravity’s not affecting this here, so the only thing attracting them is the force of electricity.1932

If they’ve got an attractive force, what’s that mean about those charges? They’ve got to be opposite. We know q1 and q2 have to be opposite.1938

One might be positive, one might be negative or it might be negative and then positive but we do know that they’re not the same type.1946

At first they’ve got an attractive force of .15 Newtons. They are then connected by a very thin wire which will allow for conduction.1953

One of them has a bunch of positive charge; the other one has a bunch of negative charge. Remember, positive charge wants to get away from all of its other positive charge friends.1962

The negative charge, I guess I should say more enemies because they’re trying to flee one another, and the negative charge is trying to get away from the other negatives.1970

They flee onto the other side and we’re going to get that they’re going to add together. We’re going to get it spread out. Since we’ve got identical metal spheres we know that we’re going to get identical spreading.1976

The final charge on each of them, q final, qf is going to be whatever was on q1 plus whatever was on q2 divided by 2.1986

It’s going to be the average of those two charges because it’s going to be evenly spread out. They’re both going to have to get the average otherwise we’re not going to have even spreading.1997

Notice that this means we’re going to have a pretty small amount of charge in the end because one of those was negative eventually.2005

The total amount of charge, total net charge is going to have to be less than what we had as the net charge on each of them originally.2010

The wire is removed and we’ll assume it’s a very thin wire so we don’t have to worry about any real charge being taken away on that wire once it goes away.2023

Because there would a few elementary charges strung along that but we’re going to assume it’s so thin, so small very few are going to wind up being left there, they’re almost entirely going to be on the spheres.2032

Finally the spheres repel each other with a force of .03 Newtons. If the charge on them is positive at the end, what were the initial charges?2045

At the end we’ve got positive charge so that means that we know qf is positive and now we’re ready to start working this out.2055

We’ve got the distance between them is .7 meters. The initial force is -.15 Newtons. That’s a really key thing to notice, is it isn’t positive because it’s attractive.2064

We haven’t really talked about how we tell where…we’ve only talked in terms of magnitude. A magnitude of -.15 is the same as +.15.2077

Notice if we plug in q1 as positive and q2 as negative or q1 as negative and q2 as positive, the important thing is that they have opposite signs.2085

If we plug in opposite sign charges we’re going to have to get a negative force from that formula otherwise things are going to break.2094

An attractive force is always going to be given by a negative value. That’s an important thing to keep in mind.2101

An attractive force will be spit out when we get a negative value and repulsive force will be spit out when we get a positive value.2107

A little bit different than what we were working with gravity where we always had attractive force because even though it always spit out positive.2115

It’s an important thing to keep in mind is suddenly it sort of comes up because the way we’ve talked about it. We’ve never introduced some of the mathematical machinery necessary to skip this issue but it is okay.2120

Just remember that it’s got to be negative if it’s attracting. Positive if it’s repulsive. Then it’s up to you to pay attention to where it’s pointing based on how the problem is set up.2133

If we’ve got this then we know that we can figure out qf now. Because force final is 0.03, a positive force because it’s repulsive.2147

K q final x q final, because its q final on both of them divided by that distance squared.2159

We solve for q final we’ll get r² 0.03 / k = qf². We take the square root of this; we plug in the numbers we’ve got.2167

0.7² x 0.03 divided by the electrostatic constant. Solve that out and notice that since we took the square root of both sides we could actually have +/-.2181

But we know for sure already this has to be a positive number because we were told that at the end charges were positive on each sphere.2199

We know that q final has to be wind up being positive. We’ve got 1.28 x 10^-6 coulombs.2209

That’s what the final charge is. Now we can use that to work to figuring out what the initial charges were.2220

Notice if qf equals q1 + q2 / 2 then we can solve for q2 to plug it in.2226

Lets look first at our initial force was -0.15 = k q1 q2 / r². To solve this equation we’re going to either have to get rid of q2 or get rid of q1.2234

To do that we use the fact that we know q final is equal to q1 + q2 / 2. So 2qf = q1 + q2.2251

We can say q2 = 2qf – q1. This isn’t a problem anymore because we know what qf is.2261

If we know what qf is we can throw that in down the road. Now we can just toss in what we’ve got.2277

-0.15 lets simplify this a little bit as we go. Move r², move that k. So we’re going to have q1 times what we sub in for q2, which is 2qf – q1.2282

We multiply that q1 over. We get r² -0.15. Let’s move that negative out front. Negative over k equals 2qf q1 – q1².2300

At this point we’ll move everything over to one side because what we’ve got now is we’ve got a quadratic formula….we’ve got a quadratic equation at this point.2320

We’re going to have to use either the quadratic formula or some sort of calculator that an impressive amount of algebraic solving in it.2331

We’ve got q1²; we keep moving this over because we want to have this equal to zero. Minus 2qf q1 – r² 0.15 / k.2338

Let’s substitute in all the values we know and it equals zero. We’ve got an equation here, so we substitute in all the values we know.2356

q1² - 2qf was 1.28 x 10^-6. Q1 - r² 0.7² 0.15 over the electrostatic constant 8.99 x 10^9 equals 0.2363

This is pretty ugly. I’ll be honest it’s not a very easy thing to solve. Not very fast, not very quick, but we’ve got some squared number, we’ve got some other number in front of….2387

We’ve got q1². Some number in front of q1 by itself and some constant. We can figure out what each one of these values is and we can either plug it into the quadratic formula or if you’ve got some sort of powerful calculator you could use an algebraic solver on that calculator to solve this whole equation.2403

If you do either one of those you’ll find out that the two possibilities for q1 is q1 is equal to either -1.85 x 10^-6 coulombs or +4.41 x 10^-6 coulombs.2419

We’ve got two different possibilities here. So how do we know which one to choose?2446

Well one thing to notice is that we could have also done this another way where we could have broken qf and we could have solved for q1 and we would have gotten q1 is equal to 2qf – q2.2451

So they’re symmetrical, so however we did this, one of them….this is going to be one of those charges will be -1.85 x 10^-6 and the other one is going to be other one.2464

We don’t know which charge was on which sphere and we can’t know that without getting a little more information but we do know that the two charges are going to have to be +4.41 x 10^-6 coulombs and -1.85 x 10^-6 coulombs.2474

Alright, hope that made sense, hope you have a better understanding of how electricity works and we’ve got a lot more to cover in it.2489

Alright, thanks, see you on educator.com later.2493